Recently, the null category noise model has been proposed as a simple and elegant solution to the problem of incorporating unlabeled data into a Gaussian process (GP) classification model. In this paper, we show how this binary likelihood model can be generalised to the multi-class setting through the use of the multinomial probit GP classifier. We present a Gibbs sampling scheme for sampling the GP parameters and also derive a more efficient variational updating scheme. We find that the performance improvement is roughly con- sistent with that observed in binary classification and that there is no significant difference in classification performance between the Gibbs sampling and variational schemes.