Will multiple radiomic sets conflict with one another? I use a single radiomic (Sennheiser AVX) but now need a second one. Will the second conflict with the first one in terms of frequencies? Or would they automatically find different frequencies to operate on?

Update: now operating two Senn AVX sets, and they work together perfectly.
These wireless microphones specifically designed not to interfere with each other. They will automatically find their counterparts but can only send a signal to one receiver.
You should be OK.