Preliminary microbiological diagnosis usually relies on microscopic examination and, due to the routine culture and bacteriological examination, lasts up to 11 days. Hence, many deep learning methods based on microscopic images were recently introduced to replace the time-consuming bacteriological examination. They shorten the diagnosis by 1-2 days but still require iterative culture to obtain monoculture samples. In this work, we present a feasibility study for further shortening the diagnosis time by analyzing polyculture images. It is possible with multi-MIL, a novel multi-label classification method based on multiple instance learning. To evaluate our approach, we introduce a dataset containing microscopic images for all combinations of four considered bacteria species. We obtain ROC AUC above 0.9, proving the feasibility of the method and opening the path for future experiments with a larger number of species.