As far as I'm aware, a 12 phase motor is feasible. We make 3-phase pmsms here, but my understanding is you'll likely find diminishing returns with a higher number of phases (above 3-4) due to increased conductor sizing to achieve the same power. Practically speaking, in a 12 phase motor you'd have 6 sets of anti-parallel phases so the machine would be reducible to a duplex 6-phase supply. There could be a good reason to make such a motor; maybe to split up the supply of a large motor to make it more manageable or better fault tolerance. I'm not sure. This sort of machine falls into what's called a multiplex winding.
The poles don't quite correlate to the phase count - beyond a few rules for having a balanced motor, etc - e.g. you could easily produce a 44 pole motor to run off of 3-phase ac, though you're going to run into other limiting factors with a high rotor pole count such as magnetic saturation.
I'm certainly not an expert on motors - and even less so on control electronics. Simple circuits tell me that capacitors and inductors would shift the electrical phase - though this also effectively be filtering your current. I'm not sure of the best way to condition such an input - it would also depend on the back-emf waveform. At the end of the day there's no free lunch.
As for the torque/power density, you're going to eventually run into upper limits on both the electrical and magnetic side. Both are temperature limited and have losses that would need to be taken into account.