Multi-messenger astrophysics is becoming a major avenue to explore the Universe, with the potential to span a vast range of redshifts. The growing synergies between different probes is opening new frontiers, which promise profound insights into several aspects of fundamental physics and cosmology. In this context, THESEUS will play a central role during the 2030s in detecting and localizing the electromagnetic counterparts of gravitational wave and neutrino sources that the unprecedented sensitivity of next generation detectors will discover at much higher rates than the present. Here, we review the most important target signals from multi-messenger sources that THESEUS will be able to detect and characterize, discussing detection rate expectations and scientific impact.