The general inclusion of the T-4 Operator into the coupled cluster equations requires an n(10) computational procedure, and even n(9) in the lowest order, as in the CCSDTQ-1 (coupled cluster singles, doubles, triples and lowest-order quadruples) method. That level of n-dependence makes it difficult to apply the method to larger systems. In this paper we circumvent this difficulty by a factorization approximation that requires only an n(7) procedure, but that provides results nearly identical to those obtained with the CCSDTQ-1 method. This observation offers a practical and accurate method to go beyond the CCSDT (coupled cluster singles, doubles and triples) approach. We also consider noniterative CCSDT(Q(f)) (coupled cluster singles, doubles, triples and noniterative quadruples) and CCSD(TQ(f)) (coupled cluster singles and doubles with noniterative triples and quadruples) methods.