  Plabic graphs are interesting combinatorial objects used to study the totally
nonnegative Grassmannian. Faces of plabic graphs are labeled by $k$-element
sets of positive integers, and a collection of such $k$-element sets are the
face labels of a plabic graph if that collection forms a maximal weakly
separated collection. There are moves that one can apply to plabic graphs, and
thus to maximal weakly separated collections, analogous to mutations of seeds
in cluster algebras. In this short note, we show that if two maximal weakly
separated collections can be mutated from one to another, then one can do so
while freezing the face labels they have in common.
