If pieces of different colors can be on the same square, there must be a rule that says how many, and whether they must all be of the same color; and there must be another rule dealing with captures on crowded squares. Therefore at least two rules are required for any game of Crowd Chess.
While examining the different possible variations of these two rules, I came up with Safety in Numbers Chess (along with some other ideas, which will follow).
There are two parts to the rule about moving multiple pieces onto the same square.
The first part is that if there are already multiple pieces on a square, and if there is also an enemy piece on the square, any piece may move onto the square, using either its movement power or its capture power. Notice that if you have several pieces on the same square, but there are no enemy pieces there, no more of your pieces may join the crowd.
Most pieces move exactly the same way that they capture, but one notable exception is the Pawn. Suppose we take the opening position and put both Kings on f3; now the Pawns at e2 or g2 can move to f3, joining the crowd, by using their capturing power; or, the Pawn at f2 can move to f3 by using its movement power. The Knight at g1 can join the crowd at f3 by using either its movement power or its capturing power, because they are the same.
The second part is that when there is one enemy piece on a square, if one of your pieces has a movement power that is different than its capture power, and can move to that square but not capture there, it may move onto the same square as the enemy piece.
For example, imagine the opening position with a Black Rook on f3; the Pawn at f2 can move to f3, creating a crowd, or the Pawns at e2 or g2 can capture at f3 -- but they may not move to f3 without capturing; or the Knight at g1 can capture at f3.
That's it, there are no more rules.
These moves are not chosen to be good moves; rather, they are chosen to illustrate the rules of the game.3...d7-d5 4 Ke1-e2?!? Qd8-e7? 5 Ke2-e3 Qe7-e4+
Black's move creates a crowd which White is glad to join. Now the Knight and the Pawn are both centralized and safe. Of course, if one of them takes advantage of its centralized position to leave e4, the crowd is diminished, and if the Black Pawn has also left, the Knight or Pawn can't rejoin the crowd on e4.
Good heavens! is it checkmate? Of course not, the King simply goes to e4, and after 6 Ke3-e4, White has the advantage of a well-protected King. At the small cost of keeping the Pawn on e4, he is safe until the endgame, at which time it will be profitable to have a centralized King. Meanwhile, the Knight is now free to leave e4, even if the Black pieces have left, without fear of breaking up the crowd; adding another piece to a crowd in order to increase the activity of the pieces already there is exactly like the idea of overprotection!
Another important implication of these rules is that Pawns can never be blockaded. After 1. e5 e6 2. d4 d5 3. e5, the Pawn chain is not a static feature of the position; instead, it is extremely fluid and both players will constantly be thinking about the right moment to advance d5-d4 or d4-d5 or e5-e6 or e6-e5 -- you cannot choose a move without thinking about all 4 possibilities!
Because Pawns can never be blockaded, a passed Pawn is considerably more threatening in this game than in FIDE Chess. In fact, not only can't Pawns be blockaded, but attempting to do so merely invites the Pawn to advance and find safety in numbers!
The sample game 1. e4 e5 2. e4-e5? Nc6 3 Nf3? e5-e4! demonstrates the tactic of breaking up a crowd.
The Pao is another example of a piece that whose movement and capture powers are different, and which therefore can start a crowd.
Safety in Numbers Chess with Different Armies should be playable because the well-known armies should maintain their parity.