We consider a generalization of the classic two-slot user cooperation model with a target to maximize the throughput. By allowing the relay to transmit, in the second time slot, an arbitrary combination of the partner's data and its new data, we show that the system throughput, which accounts for both the information rate and the outage probability, is in general improved. We further generalize the model to a multiple-user cooperative chain, where a user is given the freedom to, in its designated time slot, relay for any one, some or all of the previous users and at the same time transmit new data. Two specific time allocation methods are discussed with a sliding-window implementation, and their performances analyzed with respect to the availability of the feedback information. Compared to the conventional model, the generalized model considerably increases the system throughput, in addition to increasing the operational flexibility. Computer simulations using practical channel codes confirm the analysis.