The multinomial model is used to study the dependence relationship between a categorical response variable with more than two categories and a set of explicative variables. In presence of multicollinearity, the estimation of the multinomial model parameters becomes inaccurate. To solve this problem we develop an extension of Principal Component Logistic Regression (PCLR), model proposed by Aguilera et al. (2006). Finally a case study illustrates the advantages of the method.