Each turn, you recive two zorkmids in cash for each piece except your King; then you make a legal move; then you pay rent for every square you occupy, including the square the King is on -- edge squares cost 1, center squares cost 4, and so on. (The average price is 120 divided by 64.)
If you don't have enough money to pay your rent you must remove one or more of your pieces; it's your choice, so perhaps you can give discovered check and win by bankruptcy. If you have no pieces to remove you lose by bankruptcy (of course you cannot remove your King; and of course you cannot remove your pieces unless you are out of cash.)
You start the game earning exactly enough money to pay the average rent for 16 pieces randomly spread around the board, but as soon as some pieces are exchanged you do not have enough money to pay for an average-priced square for every piece. The endgame King versus King is not a draw! -- the player with the smaller treasury loses.
The advantages of centralization are balanced by the higher costs of occupying central squares, as you struggle to either win the midgame or build a large surplus for the endgame. This strategical tension is the theme of Rental Chess.
Rental Chess appears to be value-preserving, and therefore you can play Rental Chess with Different Armies.
The above is the simple form of Rental Chess, which appears to be quite a good game; now for some subvariants.
However, I think that this would spoil the game somewhat. The ending K versus K would now be a draw, and so the strategic game of Rental Chess would be gone; but on the other hand, the problems of the middle game would be unique and so Rental Taxi Chess would still be interesting.
Unfortunately, calculating all the rents in this form of the game requires a lot of tedious arithmetic. Probably nobody would like to play it.
But that brings me back to talking about multiple pieces on one square, and so I'll let you guess the rules of Roomie Chess -- I'll look for your guesses in the feedback section.