Before revision:  We show that if a subnetwork admits multiple nondegenerate positive steady states, then these steady states can be extended to establish multistationarity of a larger network, provided that the two networks share the same stoichiometric subspace.
After revision:  Our main result states that the answer to this question is `yes' in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple nondegenerate positive steady states, then these steady states can be extended to establish multistationarity of a larger network, provided that the two networks share the same stoichiometric subspace.