However, the convergence of the MBE is often slow and the inclusion of three-body and possibly even four-body contributions can be necessary to achieve sufficient accuracy. Therefore, several strategies exist for accelerating the convergence of the MBE, such as the application of suitable embedding schemes in the fragment calculations, the use of multilevel schemes to approximate higher-order contributions, and the use of overlapping fragments. Motivated by the observation that an MBE of the electron density seems to converge faster with the expansion order than a conventional energy-based MBE (eb-MBE), our group devised the density-based MBE (db-MBE). It is inspired by subsystem density-functional theory (DFT) and applies the total energy functional of DFT to the many-body expanded electron density. This way, a density-dependent correction to the conventional eb-MBE can be derived that accounts for higher-order interactions between the fragments by means of orbital-free DFT.