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We argue that the recently discovered bilinear superintegrabilityarXiv:2206.02045 generalizes, in a non-trivial way, to monomial matrix modelsin pure phase. The structure is much richer: for the trivial core Schurfunctions required modifications are minor, and the only new ingredient is acertain (contour-dependent) permutation matrix; for non-trivial-core Schurfunctions, in both bi-linear and tri-linear averages the deformation is morecomplicated: averages acquire extra N-dependent factors and selection rule isless straightforward to imply.

On bilinear superintegrability for monomial matrix models in pure phase