P could represent Puppet Master, a bit of a stretch as PM would make more sense grammatically, but it could get confused with Prime Minister. If referring to an individual, P, as we refer to Q, could stand for Puppet-Master. At the top of the pyramid, the top of the power structure, there must be one person pulling the strings; these people do not share power. Think back to the Nazi party and Hitler, I somehow doubt the real string puller would ever make himself/herself known publicly, why would they have to?
There are a lot of assumptions being made, Q team has done an incredible job, but do they have the whole picture yet? Bringing in and interrogating Soros implies they do not. Why does the Vatican own an infrared telescope called Lucifer? What was Lucifer really? Red Dragon, Lucifer, Red Kachina, why are they fighting for Antarctica?