  We consider the 4D Mart\'{\i}nez Alonso-Shabat equation $u_{ty} = u_z u_{xy}
- u_y u_{xz}$ (also referred to as the universal hierarchy equation) and using
its known Lax pair construct two infinite-dimensional differential coverings
over $\mathcal{E}$. In these coverings, we give a complete description of the
Lie algebras of nonlocal symmetries. In particular, our results generalize the
ones obtained in [O.I.Morozov, A.Sergyeyev, The four-dimensional Mart\'{\i}nez
Alonso-shabat equation: reductions and nonlocal symmetries. J. of Geom. and
Phys. 85 (2014), 40--45 (arXiv:1401.7942v2)] and contain the constructed there
infinite hierarchy of commuting symmetries as a subalgebra in a much bigger Lie
algebra.
