We show how a single Keller-Segel model with rotational flux terms can be used to answer the questions of global existence and blow-up of solutions for several others Keller-Segel-type models arising in mathematical biology and physics. In the case of aggregation of two species on a two-dimensional domain, we identify a threshold curve in the plane of masses that allows us to determine whether the solution of the system blows up or is global in time. As a byproduct, our research provides a novel blow up result for a mathematical model recently introduced in the literature describing the dynamics of two types of Brownian vortices with different signs.