A switching network includes an upper tier and a lower tier including a plurality of lower tier entities. A master switch in the upper tier, which has a plurality of ports each coupled to a respective lower tier entity, implements on each of the ports a plurality of virtual ports each corresponding to a respective one of a plurality of remote physical interfaces (RPIs) at the lower tier entity coupled to that port. Data traffic communicated between the master switch and RPIs is queued within virtual ports that correspond to the RPIs on lower tier entities with which the data traffic is communicated. The master switch enforces priority-based flow control (PFC) on data traffic of a given virtual port by transmitting, to a lower tier entity on which a corresponding RPI resides, a PFC data frame specifying priorities for at least two different classes of data traffic communicated by the particular RPI.