Magical Triplet Conjecture for $s$-equivalent multisets

Let $s>2$ and $n>2s$, and let an $n$-multiset be a multiset with $n$ elements. Two $n$-multisets are $s$-equivalent when they have the same multiset of $s$-sums. Magical Triplet Conjecture. For any three distinct $n$-multisets, some two of them are not $s$-equivalent to each other. This proposes an update to an earlier question about the number of mutually $s$-equivalent multisets; it remains open in the supplied text.