- This paper concerns itself with construction and study of multiple steady states, occurring in one-dimensional ambipolar electrodiffusion with local electroneutrality, constant and equal charge carrier mobilities in the absence of generation-recombination. Piecewise constant fixed change density with four sign alterations is assumed. Multiple solution branches are constructed via a numerical and asymptotic solution of a system of nonlinear equations, resulting from an explicit integration of the appropriate boundary value problem. The parameter range in which multiplicity occurs is determined with the aid of asymptotic procedures. Existence of the appropriate multiple solutions follows from the Newton-Kantorovich Theorem.