System Button CC

Hello everyone!
I’d like to find out whether there’s a way to configure the system button (the profile/page switch) so that it also sends a CC message with different values.

Practical example:
I’d like to map a Chain Selector in Ableton to different value ranges (e.g. 1–30, 31–60, 61–90, 91–127), corresponding to four different chains, each with its own synth instance. The macros for these are mapped across four different control pages on the Grid.

What I’m trying to achieve is that, when pressing the system button to switch to the next page, the same system button also sends an output message (a CC of my choice) with a different value depending on the active page (1–2–3–4), so that the correct chain is selected in line with the assigned controls.

Thanks <3