We study unconventional pairing mediated by nearly critical fluctuations of a non-superconducting order parameter that involves multiple degrees of freedom. This is motivated by the observation that superconductivity often appears close to other ordered states in experimental phase diagrams. We propose a general theory in the weak coupling regime that qualitatively connects the pairing strength with the compatibility of the pairing states and the fluctuating orders. The key ingredients are the time-reversal symmetry of the order and the superconducting fitness function. We prove our theory is universal for any electron-electron interaction which is sufficiently peaked in momentum space about the ordering vector. Our theory is applied to the spin-1/2 and spin-3/2 systems accounting for the fermiology. We propose that the superconducting fitness function can be used as a guide to identify unconventional pairing instabilities.

Keywords: fluctuating orders, unconventional superconductivity