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This is a continuation of a previous study initiated by one of us on nonlocalvertex bialgebras and smash product nonlocal vertex algebras. In this paper, westudy a notion of right $H$-comodule nonlocal vertex algebra for a nonlocalvertex bialgebra $H$ and give a construction of deformations of vertex algebraswith a right $H$-comodule nonlocal vertex algebra structure and a compatible$H$-module nonlocal vertex algebra structure. We also give a construction of$\phi$-coordinated quasi modules for smash product nonlocal vertex algebras. Asan example, we give a family of quantum vertex algebras by deforming the vertexalgebras associated to non-degenerate even lattices.

Deforming vertex algebras by vertex bialgebras