What do you mean by diferentes training and test sets? If you mean having the data ser and split into training and cross validación sets for looking clasificación performance then that is ok. Search for cross validación folds.
Keep in mind that if you use the validation test to optimize your classifer (eg by feature selection based on classification accuracy on the validation tests) you need a separate test set to get an unbiased error estimate of the classifier you builded & optimized using cross-validation