Sparse approximations to Bayesian inference for nonparametric Gaussian Process models scale linearly in the number of training points, allowing for the application of these powerful kernel-based models to large datasets. We show how to generalize the binary classification informative vector machine (IVM) (Lawrence, 2002) to multiple classes. In contrast to earlier efficient approaches to kernel-based non-binary classification, our method is a principled approximation to Bayesian inference which yields valid uncertainty estimates and allows for hyperparameter adaption via marginal likelihood maximization. While most earlier proposals suggest fitting independent binary discriminants to heuristically chosen partitions of the data and combining these in a heuristic manner, our method operates jointly on the data for all classes. Crucially, we still achieve a linear scaling in both the number of classes and the number of training points.