Here's an idea that I've been pondering for a little while...
Each player is given a fox card and a chicken card, and every player gets a stack of cards that are never revealed - they're just there to mark 'lives'. Three lives per player is probably doable with the current number of stretch extras.
When a player has lost all of their life cards, they are out of the game.
Each turn, the players openly discuss their plans, then secretly choose either their fox or chicken card, then simultaneously reveal.
If there are more foxes than chickens, the foxes start fighting each other - every player who played a fox loses a life.
If there are more chickens than foxes, the foxes have a delicious meal - every player who played a chicken loses a life.
If there's a tie, all players lose a life - UNLESS this would result in all remaining players losing their final life.
If there's only one player left in the game, he/she wins.
If there are exactly two players left, the one with the most life left is the winner. If it's a tie, deploy the tiebreaker!
One player is designated 'same' and the other is designated 'different'. The players then discuss their plans and select a fox/chicken as usual. If both players select the same animal, the 'same' player wins. I the animals are different, the 'different' player wins.
Nice idea Andrew! I shall get testing it tomorrow!