Weak attractive interactions in a spin-balanced fermion gas are known to induce a Cooper pairing instability where the fermion pairs have zero net momentum, leading to BCS superconductivity. Extensions for spin-imbalanced systems include breached superfluids, Fulde–Ferrell–Larkin–Ovchinnikov theory, and pair density wave theory. We propose a further extension of a superconducting state, dubbed a communal pairing state, whose underlying components are superpositions of Cooper pairs that share minority-spin fermions. This state includes correlations between all available fermions on both Fermi surfaces and is shown to be energetically favourable to the Fulde-Ferrell-Larkin-Ovchinnikov state. Our numerical quantum Monte Carlo study of finite spin-imbalanced systems provides clear evidence of the existence of such exotic pairing states. In spin-balanced systems, temporal fluctuations of the order parameter promote communal pairing, leading to a widening in momentum space of the superconducting gap and a decrease of the chemical potential.