Does basis set superposition error significantly affect post-CCSD(T) corrections?

We have investigated the title question for both a subset of the W4-11 total atomization energies benchmark, and for the A24x8 noncovalent interactions benchmark. Overall, counterpoise corrections to post-CCSD(T) contributions are about two orders of magnitude less important than those to the CCSD(T) interaction energy. Counterpoise corrections for connected quadruple substitutions (Q) are negligible, and (Q)_Λ - (Q) or T₄ - (Q) especially so. In contrast, for atomization energies, the T₃-(T) CP correction can reach about 0.05 ~for small basis sets like cc-pVDZ, thought it rapidly tapers off with cc-pVTZ and especially aug-cc-pVTZ basis sets. It is reduced to insignificance by the extrapolation of T₃-(T) applied in both W4 and HEAT thermochemistry protocols.