Is there a measure of this? if you wanted to keep a price at a certain level, obviously you could buy endlessly at a current price while people sell at that price until you own everything.

But let’s also assume some large proportion of players are reactionary, tending to sell when the price drops and buy more when the price rises. If you could show a sufficient demand at price A, then that large block of people would not sell their holdings because the price does not decline beyond A.

Then, the economically rational actors have a dilemma because they believe the price should be B (where B < A), but powerful actors have shown it is unlikely to drop below A for all practical transaction volumes... it may make more sense to treat the true price as A.

I guess what I’m asking is how much money relative to market cap is required to make the market accept an inflated price _without_ actually trading on it and losing money?

Yep. MS has around 27MM shares out there for stabilization pot IPO. Once they blow through that, it's the market's game.