Assume δ is a limit ordinal.

The category forcing 𝕌𝖲𝖲𝖯δ has as objects the stationary set preserving partial orders in Vδ and as arrows the complete embeddings of its elements with a stationary set preserving quotient.

We show that if δ is a super compact limit of super compact cardinals and 𝖬𝖬++ holds, then

𝕌𝖲𝖲𝖯δ completely embeds into a pre saturated tower of height δ.

We use this result to conclude that the theory of 𝖬𝖬++ is invariant with respect to stationary set preserving posets that preserve this axiom.