Can a replication subscription also be used as a publication?

Some background: We are working with a vendor who makes a read-only copy of their source database available to us in the cloud via filtered transactional replication. The cloud database is a subscriber to the source database's publications. The publishing database is multi-tenant, so only our customer data is replicated to our read-only copy. The question is: Could we could we publish from the subscriber/cloud database to a subscribing database in one of our own data centers? If so, how might that work and would it be a management nightmare?