We consider the point vortex model associated to the modified Surface Quasi-Geostrophic (mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse.