  We present numerical homotopy continuation algorithms for solving systems of
equations on a variety in the presence of a finite Khovanskii basis. These take
advantage of Anderson's flat degeneration to a toric variety. When Anderson's
degeneration embeds into projective space, our algorithm is a special case of a
general toric two-step homotopy algorithm. When Anderson's degeneration is
embedded in a weighted projective space, we explain how to lift to a projective
space and construct an appropriate modification of the toric homotopy. Our
algorithms are illustrated on several examples using Macaulay2.
