My math is rusty, but I'll do my best to make this legible:
Let there be numbers $x, y$ where $x>y$.
Let there be a finite multiset $A$ containing at least 1 element and $\exists z \in A$ where $z \geq x$.
We'll also define multiset $B$ as $A \cup \{x\}$ and multiset $C$ as $A \cup \{y\}$ .
We need as simple an example as possible of a function $f$ for which $f(A)>f(B)>f(C)$.
At the same time, for some $w$ where $\not\exists w < q, q\in A$ and multiset $D$ defined as $A \cup \{w\}$, $f(A)<f(D)$.
If certain constraints are necessary for, or would significantly simplify, the answer, feel free to present such a version too.