  In [7], Higashitani, Kummer, and Micha{\l}ek pose a conjecture about the
symmetric edge polytopes of complete multipartite graphs and confirm it for a
number of families in the bipartite case. We confirm that conjecture for a
number of new classes following the authors' methods and we present a more
general result which suggests that the methods in their current form might not
be enough to prove the conjecture in full generality.
