An extension of the spin-flip single excitation configuration interaction (SF-CIS) method is introduced. The extension, abbreviated as SF-XCIS, includes all configurations in which no more than one virtual level of the high spin triplet reference becomes occupied and no more than one doubly occupied level becomes vacant. The number of such configurations is quadratic with molecule size, and the method is implemented in a direct algorithm whose cost scales in the same way with molecule size as CIS itself, thus permitting applications to large systems. Starting from a spin restricted triplet determinant, SF-XCIS yields spin-pure singlet, triplet, and quintet states, and treats both half-occupied reference orbitals in a fully balanced way to allow application to strongly correlated problems. Tests on bond dissociation in the HF molecule, the torsional potential of ethylene, and excited states of polyenes show encouraging improvements using SF-XCIS compared to SF-CIS and a previously suggested extension, the spin-complete CIS model.