@Indnyc we actually skipped the main discussion point while discussing it.
It is impossible to do this with criteria because no one can own a criteria. That's why I thought we would be going with Himannv's suggestion of using clubs for boxes (can do countries as well).
So basically the boxes would Real Madrid, FC Barcelona, etc. So I land on Real Madrid, since it is a massively stacked club, I pay a huge amount and buy it. Now I can pick any player for Madrid. If someone else lands on that box, they would have to pay me to buy a player. But the catch there is how much do they pay me because it would grant them the same access it did to me and I paid the whole price. Generally in Monopoly I would just receive money because someone landed on my box and they don't get anything. But we need to figure out how someone gets a player on a box they don't own.
We can do that or simply assign prices with clubs, and better clubs have higher prices. So you simply have to pay the price to get a player of that club. To make things interesting we can say matches will be evaluated with the performances of the player for that club.
Basically though, having clubs/countries instead of criteria for boxes makes it much closer to the actual game and makes more sense with the money aspect.