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:  We show that if a subnetwork admits multiple nondegenerate positive steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace.