Before revision:  We show that, given a family with toric steady states and a constant number of conservation relations, we can build a chain of matroids that encodes important algebraic information regarding the steady state behaviour of the entire family  .
After revision:  We show that, given a family with toric steady states and a constant number of conservation relations, we can build a chain of matroids that encodes important algebraic information regarding the steady state behaviour of the entire family . Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks .