  We give an explicit description of the (lowering) Kashiwara operators on
Mirkovi\'c-Vilonen polytopes in types $B$ and $C$, which provides a simple
method for generating Mirkovi\'c-Vilonen polytopes inductively. This
description can be thought of as a modification of the original
Anderson-Mirkovi\'c conjecture, which Kamnitzer proved in the case of type $A$,
and presented a counterexample in the case of type $C_{3}$.
