A method for handling monotonicity constraints in optimal control problems is applied in order to correct a technical weakness of optimal nonlinear taxation models with many commodities, caused by the neglect of a second order constraint for utility maximization. We conclude that all the optimal tax-rules previously obtained remain in force under the extended approach, even without assuming that demand functions are piecewise smooth. Furthermore, in a large class of cases most of such tax-rules hold as well on intervals where the second order constraint binds. The last does not apply, however, for the celebrated zero tax-rate result at both endpoints of the tax-schedule, derived by Seade (1977) and others under the first order approach. The reason lies in the different characterization that arises with a binding monotonicity constraint, independently of the existence or not of bunching, when there are more than two goods.