Does copay accepts multiple payments?
Yes, once you have generated an address, you can have people send any number of transactions to that address from then on.  I just tried it with Copay on testnet and it works fine.  

It automatically generates a new address when a transaction arrives, just to encourage you to use fresh ones if possible, for privacy.  But previous ones continue to work indefinitely.

(Interestingly, it generates a new address whenever a transaction is received, even if that transaction was sent to an older address and the previously displayed address hadn't been used at all.)