If multiple people sign for the same output I can only accept one. After the first couple collisions I ended up listing a bunch of outputs to make collisions less likely.
Couldn't we use some of the more interesting signature types (ANYONECANPAY or something like that)? People could sign a transaction with their one input they're putting in, their output to themselves that they care about, 1 BTC to you, and you then just add your 1 BTC input from any transaction you want.