Fisher kernels combine the powers of discriminative and generative classifiers by mapping the variable-length sequences to a new fixed length feature space, called the Fisher score space. The mapping is based on a single generative model and the classifier is intrinsically binary. We propose a multi-class classification strategy that applies a multi-class classification on each Fisher score space and combines the decisions of multi-class classifiers. We experimentally show that the Fisher scores of one class provide discriminative information for the other classes as well. We compare several multi-class classification strategies for Fisher scores generated from the hidden Markov models of sign sequences. The proposed multi-class classification strategy increases the classification accuracy in comparison with the state of the art strategies based on combining binary classifiers. To reduce the computational complexity of the Fisher score extraction and the training phases, we also propose a score space selection method and show that, similar or even higher accuracies can be obtained by using only a subset of the score spaces. Based on the proposed score space selection method, a signer adaptation technique is also presented that does not require any re-training.