  In this paper, we study the global approximate multiplicative controllability
for nonlinear degenerate parabolic Cauchy-Neumann problems. First, we will
obtain embedding results for weighted Sobolev spaces, that have proved decisive
in reaching well-posedness for nonlinear degenerate problems. Then, we show
that the above systems can be steered in $L^2$ from any nonzero, nonnegative
initial state into any neighborhood of any desirable nonnegative target-state
by bilinear piecewise static controls. Moreover, we extend the above result
relaxing the sign constraint on the initial date.
