A new version of the MQCT program is presented, which includes an important addition, adiabatic trajectory approximation (AT-MQCT), in which the equations of motion for the classical and quantum parts of the system are decoupled. This method is much faster, which permits calculations for larger molecular systems and at higher collision energies than was possible before. AT-MQCT is general and can be applied to any molecule + molecule inelastic scattering problem. A benchmark study is presented for H2O + H2O rotational energy transfer, an important asymmetric-top rotor + asymmetric-top rotor collision process, a very difficult problem unamenable to the treatment by other codes that exist in the community. Our results indicate that AT-MQCT represents a reliable computational tool for prediction of collisional energy transfer between the individual rotational states of two molecules, and this is valid for all combinations of state symmetries (such as para and ortho states of each collision partner).