Individual animal recognition and re-identification from still images or video are useful for research in animal behaviour, environment preservation, biology and more. We propose to use Restricted Set Classification (RSC) for classifying multiple animals simultaneously from the same image. Our literature review revealed that this problem has not been solved thus far. We applied RSC on a koi fish video using a convolutional neural network (CNN) as the individual classifier. Our results demonstrate that RSC is significantly better than applying just the CNN, as it eliminates duplicate labels in the same image and improves the overall classification accuracy.