We present an extrapolation scheme for the correlation energy in many-body theory that requires only a relatively small fraction of the orbitals spanning the virtual space but recovers nearly the whole dynamic correlation energy, independently of the single- or multi-reference nature of the problem. Applications to both ground-state chemistry and photochemistry are discussed that clearly show how such an extrapolation scheme can be used to overcome the scaling walls in ab initio quantum chemistry arising from the sheer number of molecular orbitals needed for very accurate calculations.