In multiclass semi-supervised learning (SSL), it is sometimes the case that the number of classes present in the data is not known, and hence no labeled examples are provided for some classes. In this paper we present variants of well-known semi-supervised multiclass learning methods that are robust when the data contains an unknown number of classes. In particular, we present an “exploratory” extension of expectation-maximization (EM) that explores different numbers of classes while learning. “Exploratory” SSL greatly improves performance on three datasets in terms of F1 on the classes with seed examples—i.e., the classes which are expected to be in the data. Our Exploratory EM algorithm also outperforms a SSL method based non-parametric Bayesian clustering.