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We follow the general recipe for constructing commutative families of$W$-operators, which provides Hurwitz-like expansions in symmetric functions(Macdonald polynomials), in order to obtain a difference operator example thatgives rise to a $(q,t)$-deformation of the earlier studied models. As before, akey role is played by an appropriate deformation of the cut-and-join rotationoperator. We outline its expression both in terms of generators of the quantumtoroidal algebra and in terms of the Macdonald difference operators.

$(q,t)$-deformed (skew) Hurwitz $\tau$-functions