A previously proposed two-body fragment molecular orbital method based on the restricted Hartree-Fock (RHF) method was extended to include explicit three-body terms. The accuracy of the method was tested on a set of representative molecules: (H2O)(n), n=16, 32, and 64, as well as alpha and beta n-mers of alanine, n=10, 20, and 40, using STO-3G, 3-21G, 6-31G, and 6-31++G** basis sets. Two- and three-body results are presented separately for assigning one and two molecules (or residues) per fragment. Total energies are found to differ from the regular RHF method by at most DeltaE(2/1)=0.06, DeltaE(2/2)=0.04, DeltaE(3/1)=0.02, and DeltaE(3/2)=0.003 (a.u.); rms energy gradients differ by at most DeltaG(2/1)=0.0015, DeltaG(2/2)=0.000 75, DeltaG(3/1)=0.000 20, and DeltaG(3/2)=0.000 10 (a.u./bohr), and rms dipole moments are reproduced with at most deltaD(2/1)=3.7, deltaD(2/2)=3.4, deltaD(3/1)=2.6, and deltaD(3/2)=3.1 (%) relative error, where the subscript notation n/m refers to the n-body method based on m molecules (residues) per fragment. A few of the largest three-body calculations were performed with a separated trimer approximation, which presumably somewhat lowered the accuracy of mostly dipole moments which are very sensitive to slight variations in the density distribution. The proposed method is capable of providing sufficient chemical accuracy while providing detailed information on many-body interactions. (C) 2004 American Institute of Physics.