The Master Compressor is applied overall, and is not realtime controllable via an assigned Foot Switch. The Insertion Effects can be turned on and off via a Foot Switch, and are akin to the example you give... "when a guitar player kickes in a clean-drive pedal for a boost during their solos".

From the Reference Manual page 6:
The FC4 and FC5 (sold separately) can be connected via the [ASSIGNABLE] FOOT SWITCH jack so that various functions can be assigned to them. For example, on the Controller screen (page 21) from the Performance Part Edit area, you can assign on/off switching of an insertion effect (page 11) to one of these foot switches.

The guitar player does not have realtime control over anything but the effects inserted inline with their guitar signal. The definition of Insertion Effects is those you wish to adjust in realtime, exactly as your example states.

The MASTER COMP, like the MASTER EQ, applies to all instrument currently in the CP4 Stage's three Part mixer. If you wish to have a Foot Switch to control an Effect on one of the Parts, apply it as an Insertion Effect on that particular Part and program the FS to control that effect.

If that is not possible (because you are doing something else with the Insert Effects), simply manually press the [MASTER COMP] button to engage the boost just before you begin your solo.

Hope that helps.

Thanks very much for the clarification. Your explanation makes sense. I've read the manual a few times but just wasn't sure if I was missing something.
This forum and your responses have taught me a lot about my new piano. We're very fortunate to have this forum and the many valuable responses available to us.
Thanks again.

KJ