A. Rabinovich, and B. A. Trakhtenbrot, in their Behavior Structures and Nets paper, uses the expression "partial multiset" without defining it.
In context, they have an alphabet $\Sigma$, a finite multiset $A$ over $\Sigma$, and let $B \subset A$ be a "partial multiset".
Should that be read simply as inclusion of multisets? They also discuss partial ordered multisets, but "partial" refers to the order, and not the multi-set.