  In this paper we study quasilinear elliptic equations driven by the double
phase operator along with a reaction that has a singular and a parametric
superlinear term and with a nonlinear Neumann boundary condition of critical
growth. Based on a new equivalent norm for Musielak-Orlicz Sobolev spaces and
the Nehari manifold along with the fibering method we prove the existence of at
least two weak solutions provided the parameter is sufficiently small.
