  This is a continuation of the early paper concerning matroid base polytope
decomposition. Here, we will present sufficient conditions on $M$ so its base
matroid polytope $P(M)$ has a {\em sequence} of hyperplane splits. The latter
yields to decompositions of $P(M)$ with two or more pieces for infinitely many
matroids $M$. We also present necessary conditions on the Euclidean
representation of rank three matroids $M$ for the existences of decompositions
of $P(M)$ into $2$ or $3$ pieces. Finally, we prove that $P(M_1 \oplus M_2)$
has a sequence of hyperplane splits if either $P(M_1)$ or $P(M_2)$ also has a
sequence of hyperplane splits.
