For years we have seen the shorts manipulate the share price and...

For years we have seen the shorts manipulate the share price and continually push it down. So hypothetically speaking, as someone with little knowledge of how all this manipulation works, what are the chances of, and how much would it cost a well funded insto to push the share price up and hold it there, so as to cause a short squeeze?
I imagine the potential profits from a squeeze would be huge, but the investment to be able to manipulate the price in this way would also be huge. In the end it's a numbers game.
If the price can be manipulated in one direction, then in theory, it can be manipulated the other way.