The generalized molecular orbital (GMO) concept is extended to a higher order method, which begins with a pair-excited multiconfiguration self-consistent field (PEMCSCF) for the orbital optimization and is followed by a multireference configuration interaction calculation. Here, this method is referred to as GMO2. The method has the advantage of being variational, of handling large numbers of active electrons, and of only needing the user to specify the number of active electrons and orbitals without specifying a dominant MO or VB configuration. In this paper, we briefly review the PEMCSCF theory, describe in more detail a new and more efficient optimization procedure, and propose determining the energy with configuration interaction (CI) at the single, double, triple, and quadruple-excitation levels (SDTQ) as a replacement for the full CI, which is needed in a complete active space (GAS) method. Several examples of the application of the method are investigated: methane, tetrahydrogen, benzene, dinitrogen dissociation, acetylene dissociation. For the five systems studied, the PEMCSCF orbital optimization produces orbitals that only differ from those of a CASSCF by an average of 4 kcal/mol when both localized bond type or symmetry-adapted orbitals are used in a full CI, GMO2(FCI). The additional error of replacing full CI with a SDTQ CI, GMO2(SDTQ), is usually less than 1 kcal/mol.