This work presents an investigation on the scalability of a deep leaning (DL)-based blind transmitter positioning system for addressing the multi transmitter localization (MLT) problem. The proposed approach is able to estimate relative coordinates of non-cooperative active transmitters based solely on received signal strength measurements collected by a wireless sensor network. A performance comparison with two other solutions of the MLT problem are presented for demonstrating the benefits with respect to scalability of the DL approach. Our investigation aims at highlighting the potential of DL to be a key technique that is able to provide a low complexity, accurate and reliable transmitter positioning service for improving future wireless communications systems.