Let $h_0 > 0$, let $m: T^*\mathbb{R}^n \to (0,\infty)$ be an order function, and let $S(m)$ denote the semiclassical symbol class on $T^*\mathbb{R}^n$ for parameters $0 < h \le h_0$. Let $(a_j)_{j \ge 0}$ be a sequence of $h$-independent symbols, with each $a_j \in S(m)$, viewed as the constant family