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.