No mute/solo recording i’m afraid..
Darn.
You can control mutes from an external midi note source, so you could probably rig up up an external solo-like midi function as well (solo being an inverse of mute).
I haven't tried this, but if you are in Playlist mode the external midi control of mutes may still work. Check the system settings to assign how the external midi note control works. You can select between 'follow pad func', 'sound', 'beats' or 'mutes'.