Yes. For this, you need to set an offer as CPS and add the set txid parameter to the postback on the affiliate network. The unique combination of tid+txid will bring you several conversions from one click ID. As for CPA offers, there can't be several conversions by one and the same tid (it is possible only if you use conversion status, but in this case, only 1 of these conversions will be approved and recorded in your income).
Can there be several conversions by one and the same tid?