You can do this via automations in HA (different buttons emit different signals on press, hold etc, check out the documentation here), but here’s how I did it in the Phoscon UI:
When you have a light group selected, click the “link switch” button, select a key, and what you want to assign it to. Select a different group, link switch, select another key, and a command. Using this pattern I can now control 4 different groups of lights (using the option to long press for dimming and regular press for on/off). Middle button (power) switches all lights on/off.
I realize when I re-read your question that maybe want to be able to control multiple aspects of several groups simultaneously – I think you can do stuff with AppDaemon if you want even more control.