After the fundamental work of Demailly on approximations, it is a natural question to ask which plurisubharmonic functions admit a `nice' approximation in the sense of a decreasing equisingular approximation with analytic singularities. For arbitrary toric plurisubharmonic functions, we give a criterion for admitting a nice approximation with toric approximants. Our results are motivated by a recent result of Guan for toric plurisubharmonic functions of the diagonal type. This is joint work with Jongbong An.