In chess can you or your opponent have more than one queen?
Theoretically you could have 9 queens and so could your opponent since pawns get promoted to a piece of your choice when they get to the other side.
If you get the pawn to the other side, you get a free knight or queen.
You can actually promote to a rook, bishop, queen, or knight.
When it's down to my last pawn and my opponents lost all his pieces I'll sometime take a rook instead of a queen, it eliminates the chance of a stalemate.
Stalemate shouldn't be a problem. You just need to be a little careful.