A Network Interface (NI) includes a host interface, which is configured to receive from a host processor of a node one or more cross-channel work requests that are derived from an operation to be executed by the node. The NI includes a plurality of work queues for carrying out transport channels to one or more peer nodes over a network. The NI further includes control circuitry, which is configured to accept the cross-channel work requests via the host interface, and to execute the cross-channel work requests using the work queues by controlling an advance of at least a given work queue according to an advancing condition, which depends on a completion status of one or more other work queues, so as to carry out the operation.