In electronic structure theory, restricted single-reference coupled cluster (CC) captures weak correlation but fails catastrophically under strong correlation. Spin-projected unrestricted Hartree-Fock (SUHF), on the other hand, misses weak correlation but captures a large portion of strong correlation. The theoretical description of many important processes, e.g. molecular dissociation, requires a method capable of accurately capturing both weak- and strong correlation simultaneously, and would likely benefit from a combined CC-SUHF approach. Based on what we have recently learned about SUHF written as particle-hole excitations out of a symmetry-adapted reference determinant, we here propose a heuristic coupled cluster doubles model to attenuate the dominant spin collective channel of the quadratic terms in the coupled cluster equations. Proof of principle results presented here are encouraging and point to several paths forward for improving the method further.