My guess is that the Parts not being affected by sliders have been assigned to the super knob

Cutting to the chase - select Part 4 (the bass) and turn Assignable Knob 6 full counter-clockwise (set it to 0). Now slider 4 controls the bass volume as you would expect.

To go into gory detail ....

My guess is that the Parts not being affected by sliders have been assigned to the super knob

That's a reasonable guess - but not correct. In the general sense when there's a "ghost in the machine" like this - you can bet that there is another controller offsetting the parameter that you assume you have full control over. In this case, the Part volumes are mapped to sliders - and, naturally, you would assume the sliders would do what sliders do. However, the fact remains that there may be other influences to part volume apart from the sliders.

There's no real ghost in the machine - just the need to discover what is having an influence on the parameter that you assume you have full control over with another controller. If something seems "off" - you probably don't have full control with your assumed controller (like the sliders) - you have shared/partial control.

These other influences don't "take over" the control. Each contribution to the target parameter (Part 4 volume in this case) works together in an additive manner. One influence CAN add so much to the value that there's "no way" for the other controller to affect the final outcome. In a sense, this is "taking over". However, in the literal sense - no influence takes over. They just add together and you get what you get.

Lets walk through this discovery process.

First, we start with identifying the Part we're interested in is "Imperial Jazz Trio" Part 4. That's the bass. The head scratcher is that the slider cannot change the volume. So we know that the parameter we want to look for is Part 4 "Volume". Lets go look for it.

1) Press [PERFORMANCE] (HOME) button - that puts you in the home screen. A good level-set start for just about anything dealing with Parts.
2) Touch the touchscreen (TS) Part 4 area in order to select it. The system will draw a white box around it and pop up a series of options including "Edit". Touch the "Edit" popup option
3) TS: navigate to the menus "Mod/Control" -> "Control Assign". If you don't see these - make sure the "Common" button on the bottom row is selected. This "Control Assign" menu is where you will discover your "ghosts". This is the area where we can see what parameters ("destinations" ) are influenced by what controllers ("sources" ). Some parameters will always be influenced by a built-in controller. Like how the slider affects Part volume. These associations are NOT shown in the "Control Assign" area. This area is only for custom assignments on top of those that are built-in.
4) TS: Now in "Control Assign" touch the "Display Filter" and change it to "All". What this does is the system will now show ALL of the destinations for this Part no matter what the source is. Where you see "Destination #" (where # is 1-16) near the top of the screen - there is also a button to scroll through what will commonly be multiple pages of destinations when displaying "All". The Page number is just above the row of Destinations and to the right of the page number is a touchscreen area you can press " > " to scroll to the next page of destinations. What I would do here is scan through the destination parameters (the destination parameter is shown just below the destination number) and look for your "ghost". Again, here we are looking for "Volume". All of these destinations are at the Part level (Part 4 level, in fact) so you can add "Part 4" to the front of each parameter name in your head. When you scan the 1st page of destinations in this example Part 4 of "Imperial Jazz Trio" - you don't see "Volume". Keep looking
5) TS: Touch the Page " > " touchscreen area to scroll through the pages. Looking for your destination parameter as you go. In our example, the 2nd page (Destination #7) shows "Volume" (aka - adding the other context: Part 4 Volume destination offset). Ok - we found it. Lets discover what is influencing Part 4's volume other than the sliders.
6) TS: Once found, touch the destination that matches the parameter you're looking for. Touching "Volume" the bottom of the screen will now populate with information specific to this destination (destination #7 in "Imperial Jazz Trio" )
General note - in the general case, we wouldn't be satisfied with finding the first match of the parameter we're looking for. The system can (meaning able to - but a programmer may not necessarily do this) assign the same destination parameter multiple times. There may be more than one source for the same destination - or even the same same source multiple times for the same destination. So keep scanning through ALL of the destination parameters to make sure, in the general case, you find all of the influences on the parameter you are interested in. Here - for Imperial Jazz Trio - there's only this one.
7) TS: Look for the "Source" box. This tells you what is influencing (modulating) this parameter. I hesitate to say "controlling" because that implies exclusivity. It's controlling, OK - but shared with other things also controlling. So I say "influencing" as perhaps a more accurate description. For Destination #7 (Volume) here - we see the Source is set to "AsgnKnob 6" - Assignable Knob #6. Now it's important to take a quick pause here to talk about assignable knobs.

--- aside ---

You have 4 physical knobs on MODX. There are actually 8 total knobs with these 4 physical knobs representing 1-4 or 5-8. That's one level of the knob story. So in total, you have a total collection of 8 knobs you can turn (4 at any one time banked between two halves).

The other level of the knob story is that this collection of 8 knobs can assume different modes. These 8 knobs are not always controlling the same thing. You have LEDs on your keyboard that tell you which mode these 8 knobs are in. The 8 knobs can represent the assignable knobs of the currently selected Part (Part Assignable Knobs) OR the 8 knobs can represent the assignable knobs of the entire Performance (Common Assignable Knobs) OR the 8 knobs can represent one of 4 "fixed functions" (TONE ; EG/FX ; EQ ; ARP/MS)

It's easy to tell if the knobs are NOT in the mode of either of the two Assignable Knob modes. You will see a green LED next to the fixed-function that the knobs are assigned to (either tone OR eg/fx OR eq OR arp/ms) and you will also see just to the left of each of the 4 knobs the [ASSIGN] button is OFF (not lit amber).

If the [ASSIGN] button is lit amber - then you know that the knobs are set to one of the two Assignable Knob modes (either Part-level OR Common-Level) - but you don't know which without more context. While you're editing a PART - as you are right now in this step - the knobs will be set to the mode of Part Assignable Knobs. When you press the [PERFORMANCE] (HOME) button, this will de-select all Parts and then the knobs will be in the mode of Common Assignable Knobs. Selecting and de-selecting Parts is the only way to change these modes. Pressing [PERFORMANCE] (HOME) is the easiest way to de-select. To select any given Part - the easiest way to to touch one of the Parts after first pushing the [PERFORMANCE] (HOME) button. Montage, with more buttons, has a few other choices for display/selection that I won't get into here.

--- back to it ---

Within the context of this screen - remember we add "Part 4 ..." to all the parameter names. So this "AsgnKnob 6" SOURCE is Part 4 Assignable Knob #6. Now we know that the Part 4's own assignable knob #6 has an influence on the bass's volume.
8) Knowing that Part 4 Assignable Knob #6 has an influence on volume - you'll want to put your Sherlock Holmes hat on and start doing some deeper forensics. At least to really solve this mystery. You will want to know two things: what is the current position of the influencing source controller (Part 4 Assignable Knob #6 in this case) and also - at the position of this source controller - what is the degree of influence (offset value) to the destination parameter? The second question doesn't have a black-and-white answer because the system doesn't tell you the exact value. We'll have to ballpark it in most cases. That's good enough for this mystery.
8a) What's the controller set to (Part 4 Assignable Knob #6)? There are different ways to do this. Quick-and-dirty is to - since were were last left editing Part 4 - check the [ASSIGN] button is lit (to left of the 4 knobs) and press it if it is not - then select the bank 5-8 of the knobs and turn Knob #6 ever so slightly. MODX I believe shows you the value of the knob on the screen since there are no LEDs like Montage. That's quick-and-dirty. A more methodical way would be: i) Press [PERFORMANCE] (HOME) to go back to the home screen. ii) TS: Touch Part 4 - do not select anything after the popup comes up. You can press the [EXIT] button below the DATA DIAL to get rid of the menu if you want. iii) Make sure the [ASSIGN] button is lit and press it if it isn't, iv) Notice just below the Performance name "Imperial Jazz Trio" are 8 circles and to the left of these circles is the label "Part 4 Assign". These are the values of the 8 Assignable knobs. Look at #6 which is in the same column as the empty Part 6 in this Performance. That's the SOURCE controller value. It should read "127" by default if you haven't moved it. That happens to be cranked all the way "up" to the maximum value. Logic would say that's a lot of influence - and, as we'll find out, it is.
8b) What's the offset of the destination parameter (Volume) when the SOURCE (Part 4 Assignable Knob #6) is at 127? Lets find out. Navigate back to the "Control Assign" menu. [PERFORMANCE] (HOME) - you're already here - then TS: Touch Part 4, Select "Edit" from the popup, then navigate to the menu "Mod/Control" -> "Control Assign". We're back where we once were. Find destination #7 again. You could, this time, set "Auto Select" (near the upper-left corner) to ON - it will be a blueish green color, not grey. Then once ON, spin Knob #6 to the right while the [ASSIGN] button is lit. This will engage Part 4 Assignable Knob #6 and automatically filter all destinations associated with this SOURCE controller. You will see Destination #7: (Part 4) Volume. Sometimes you will see multiple destinations - and maybe even multiple pages for the same controller. Touch the destination you are interested in to be sure all of the information about this destination is displayed.

8b is kind of long - because it's a deeper dive kind of thing. Forensics. Here's a paragraph to break it up.

From here you will see the curve - it's an "X/Y" plot showing you on the X-axis (left to right) the SOURCE controller's input value. All the way to the left of this graph is SOURCE controller (also called "input" ) = 0. All the way to the right of this graph is SOURCE controller = 127. That's true irrespective of any settings. The graph (curve) shows values above the horizon and below the horizon. This is the Y-axis value and where the curve displays on the Y-axis is a representation of the DESTINATION's offset. Above the horizon is a positive offset and below the horizon a negative one. Right on the horizon and this is a 0 offset (no change). The way you would read this is that IF the controller is currently at THIS (choose a space in the left/right direction) place on the x-axis, then the graph shows (by height) what the value of the offset will be. Either positive or negative. This particular curve for our volume parameter shows only positive values. All the way on the left-hand side (assignable knob = 0, or fully counter-clockwise) the graph shows no height at all. This is an output value (parameter offset value) of 0. Then as we turn the knob clockwise we start moving along the curve getting higher and higher values (all above the horizon). You see the graph slopes up on an increasing curve and hits the "TOP" at some point - saturation. The value goes off the screen. We know that the controller (Part 4 Assignable Knob #6) is at 127 (full clockwise). So that means our offset will be at full saturation - maximum. +127. Whatever the volume is at - we will add +127 to the volume when the knob is at 127. So now we know.

Let's take this information and drill down involving the sliders here.

WITHOUT the offset of 127 (imagine it just vaporizes - and imagine any other possible influence on volume OTHER than the slider vaporizes) - then the slider is the only determining factor of Part 4's Volume. Slide the slider all the way "down". The volume of the Part is now at 0. When the slider is all the way down - the volume is 0. When the slider is all the way up - the volume is 127. When slider is in the middle - the volume is 64. And so on.

So lets set the slider right in the middle. Now volume is 64. Ok - lets add back the influence of the Control Assign destination. Remember this influence with the Part 4 Assignable Knob #6 at 127 (full clockwise) is +127. We just add these together.

Slider at 50% - Volume is 64 + Destination #7 Volume influence +127 = 191. You cannot have a volume of 191 - the maximum is 127 - so these saturate. The final result is 127. (64+offset of +127 = 127). Using this methodology - try to find a slider position where you do not end up with 127. You can't. Slider=0 Volume of 64 + Destination #7 Volume influence +127 = 127 (maximum). So that Part 4 Assignable Knob #6 really has the volume in a jam.

You can manually get "rid" of the influence of Part 4 Assignable Knob #6 by turning Part 4 Assignable Knob counter-clockwise fully until the SOURCE controller (the knob) is at a value of 0. This is the input value of the curve. At an input of 0 - the curve's output (the offset applied) is 0. Now the slider has free reign to set any value from 0-127.

To be a bit more complete - set the Part 4 Assignable Knob #6 to some positive value - but not yet in the saturation zone. Maybe somewhere around 45. You'll see that you can no longer make the slider (even all the way down) achieve a silent volume. This is because of the influence of the offset. It's adding a non-zero offset. You'll notice that at some point near the "top" of the slider travel you will saturate. What I am trying to demonstrate here is that no controller "takes over" just because it's programmed. It's only that sometimes the offset applied (like when the assignable knob was at full clockwise) may saturate the value.

Some other points here - if you press [PERORMANCE] (HOME), touch the performance name "Imperial Jazz Trio" - then select Edit - you will be editing the Common/Audio section. These are the Performance-wide settings that apply to all Parts. Within this section is another "Control" -> "Control Assign" menu. This is the one that includes the Common Assignable knobs. If you filter by "All" - you will not find Part 4 Assignable Knob 6 as a destination. The only way for superknob to affect Part-level assignable knobs is for a linkage to be setup here. One of the 8 Common Assignable knobs must be the SOURCE and DESTINATION must be one of the Part's Assignable Knobs. This does not exist in this Performance (not for Part 4 Assignable Knob 6) - so we know that superknob has no influence here. Part 4's Assignable knob 6 is free to be set by itself without having something else touch it. So once you set Part 4 Assignable Knob #6 to full counter-clockwise (0) - then the slider #4 will control the bass volume - which was your original goal here.

Note that the sliders themselves can assume a few different modes. Make sure that Part 1-8 (there's an LED to the left of the sliders) is illuminated and NOT Element/Operator. Certainly make sure you have the right bank of sliders selected. This will ensure slider #4 is indeed controlling the bass volume. Once you "turn down" Part 4's Knob #6, that is.

My problem....
I can't use the Control Slider to adjust the bass volume. There are 3 parts to the piano, and I can adjust the
volume on those using the sliders, but I can't figure out how to change the bass volume using the sliders.

Anytime a Control Slider is not directly adjusting the Volume of a Part, it is because it has been reassigned to a Knob (either just a Part’s AssignKnob or additionally, the Super Knob) or another Controller.

The most efficient way to hunt this down is as follows:
From the HOME screen
Press [SHIFT] + [HOME] to see the “Motion Control” > “Overview” screen
A map of the current assignments...
Set the “Part” to “Part 4” — the Bass
You can now see what Controllers are active on Part 4

This color coded screen lets you quickly explore what’s happening...you can customize the view
Magenta = left hand Controllers
Green = Assign Knob
Amber = Fader
Blue = Super Knob

For clarity’s sake tap the word “Controller” and “Fader” to turn these OFF from view (only)

You can see Part 4 has 8 Assign Knobs (green) but no link to the Super Knob (blue)

We can take the shortcut to these assignments, by tapping the “Edit Part 4 Control Settings” box
We are looking for “Volume”

Set “Auto Select” = active (green) if not set already
Make sure [ASSIGN] is lit
Turn Part 4’s Assign Knobs to recall the assignments to the “Display Filter”, each-by-each.
Assign Knob 6 = Volume

When viewing AsgnKnob 6 in the Display Filter
Tap “Delete” in the lower right corner
This will remove this assignment and return real time Fader control over Part 4’s Volume.

Return to the HOME screen
Raise Slider 4 to your taste.
You may need to move the slider all the way down, to “catch/hook” the value and become active...
[STORE] the newly edited version to your USER BANK.

Thank you all vey much for your replies, and also for the detail in your explanations.
I do now understand where the volume "problem" was and how to fix it.

One additional question...
My understanding is that there are 8 assignable knobs, and that these knobs are 1-4, and then you have to
press a button or something which makes those same 4 knobs become 5-8, right?
So in the examples above, the issue was that the bass volume was set up to be controlled by assignable knob #6.
If I wanted to adjust the bass volume, and I leave the settings the way they originally were, how do I control knob #6?
I'm assuming that knob #6 is actually the second assignable knob from the left, but I can't figure out how to make the switch
so that those knobs become 5-8.

Thank you for your help.

Owner's manual page 32:

press the [ASSIGN] button to select Common Assign 1–4 or Common Assign 5–8.
The button lights when Assign 1–4 is selected, and the button flashes when Assign 5–8 is selected.

... this is taken from a section explaining using these knobs as Common. But you can gather from this that generically you would press the [ASSIGN] button to toggle between 1-4 or 5-8 and the [ASSIGN] button will tell you which you have selected by either staying solid (1-4) or flashing (5-8).

With the [ASSIGN] button flashing, #6 is going to be the 2nd knob from the left.

[ASSIGN] (Solid.....) : (Knob 1) (Knob 2) (Knob 3) (Knob 4)
or
[ASSIGN] (Flashing) : (Knob 5) (Knob 6) (Knob 7) (Knob 8)