  We argue that the recently discovered bilinear superintegrability
arXiv:2206.02045 generalizes, in a non-trivial way, to monomial matrix models
in pure phase. The structure is much richer: for the trivial core Schur
functions required modifications are minor, and the only new ingredient is a
certain (contour-dependent) permutation matrix; for non-trivial-core Schur
functions, in both bi-linear and tri-linear averages the deformation is more
complicated: averages acquire extra N-dependent factors and selection rule is
less straightforward to imply.
