Non-expandability conjecture for ultimately bipartite subtraction games

Let $S$ be the subtraction set of an ultimately bipartite subtraction game, meaning that its nim-sequence is eventually periodic with period two and alternates between $0$ and $1$. Non-expandability conjecture. The subtraction set $S$ is non-expandable: no additional subtraction can be added to $S$ without changing the nim-sequence. This conjecture concerns the maximality of subtraction sets realizing ultimately bipartite nim-sequences; the preceding results establish constraints on possible added subtractions, but the general claim remains open.