  The Type D asymmetric simple exclusion process (ASEP) is a particle system
involving two classes of particles that can be viewed from both a probabilistic
and an algebraic perspective (arXiv:2011.13473). From a probabilistic
perspective, we perform stochastic fusion on the Type D ASEP and analyze the
outcome on generator matrices, limits of drift speed, stationary distributions,
and Markov self-duality. From an algebraic perspective, we construct a fused
Type D ASEP system from a Casimir element of $U_q(so_6)$, using crystal bases
to analyze and manipulate various representations of $U_q(so_6)$. We conclude
that both approaches produce different processes and therefore the previous
method of arXiv:1908.02359, which analyzed the usual ASEP, does not generalize
to all finite-dimensional simple Lie algebras.
