In this paper, we analyze the problem of how to adapt the concept of priority to situations where several perfectly divisible resources have to be allocated among a certain set of agents that have exactly one claim that is used for all resources. In particular, we introduce constrained sequential priority rules and two constrained random arrival rules which extend the classical sequential priority rules and the random arrival rule to these situations. We also provide an axiomatic analysis of these rules. Finally, we present a numerical example to compare the constrained random arrival rule to other solutions in this context.