Switching HX stomp amp+cab blocks with the MC6 / MC6 pro

Does anyone know if it’s possible to switch the amp+cab used in an amp+camp block on the HX stomp via MIDI?

My specific use case is that I have a number of patches that use the C4 synth for guitar > bass sounds, but the individual C4 bass patches sound better with different amp+cab models on the HX Stomp. Can I switch the amp+cab used by the amp+cab block to allow me to have one “C4 bass synth” preset, or do I need to create “c4 bass synth ampeg”, c4 bass synth cali bass" etc, and have a separate patch for every new bass+cab block setting even though the preset is otherwise identical?

The latter is doable, esp with the expanded banks on the mc6 pro, but just wondering if it’s needed.

Thanks!

Michael