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I am not quite sure if I understand the question correctly, so first some general thoughts:

Any classifier I am aware of needs the same dimensionality of feature vectors, for each feature vector a class is predicted, i.e. having n features with dimension d, you'll get n results, this is the reason why the features will often be encoded via Bag of Words (BoW). For example in the case of instance recognition the number of features is fixed as well as the image size or image window (then the features can be reshaped to have dimensionality 1, e.g. one HoG-descriptor, or via BoW encoded).

Coming back to the other part of your question: yes random forests can be used for multiple class classification.