  The problem of Cooper instability is studied by implementing the
Kohn-Luttinger mechanism in the framework of the Shubin-Vonsowsky model taking
into account the intersite Coulomb interactions within the first and second
coordination spheres. It is shown that the Kohn-Luttinger renormalization for
the effective interaction in the second-order terms of perturbation theory, as
well as the inclusion of intersite hoppings in the second and third
coordination spheres, significantly affects the interplay between the
superconducting phases with $d_{xy}$-, $p$-, $s$-, and $d_{x^2-y^2}$-wave
symmetries of the order parameter.
