Fragmentation methods allow for the accuratequantum-chemical treatment of large molecular clusters and materials. Here, we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account of the environmentin the subsystem calculation performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the systems' total energy. This provides a correctionto the energies calculated with a conventional, energy-based MBE that only depends on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate quantum-chemical calculation of molecular clusters and materials.