It is demonstrated that a nonlinear Schrodinger equation with certain nonlinearities allows for an existence of multistable singular solitons (i.e. singular solutions with the same carried power but different propagation parameters). Using a paticular nonlinearities (the "linear smooth step"model) as an illustrative example, the switching of bistable solitons states of the highly-nonlinear (generlised) Schrodinger equation is simulated.