  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.
