Can we constrain the maximum value for the spin parameter of the super-massive objects in galactic nuclei without knowing their actual nature?

In 4-dimensional General Relativity, black holes are described by the Kerr solution and are subject to the bound $\mathrm{\mid }{a}_{\ast }\mathrm{\mid }\le 1$, where $a_{\ast }$ is the black hole spin parameter. If current black hole candidates are not the black holes predicted in General Relativity, this bound does not hold and $a_{\ast }$ might exceed 1. In this letter, I relax the Kerr black hole hypothesis and I find that the value of the spin parameter of the super-massive black hole candidates in galactic nuclei cannot be higher than about 1.2. A higher spin parameter would not be consistent with a radiative efficiency $\eta >0.15$, as observed at least for the most luminous AGN. While a rigorous proof is lacking, I conjecture that the bound $\mathrm{\mid }{a}_{\ast }\mathrm{\mid }\lesssim 1.2$ is independent of the exact nature of these objects.