  Density-dependent potentials are frequently used in materials simulations due
to their approximate description of many-body effects at minimal computational
cost. However, in order to apply such models to multi-component systems, an
appropriate definition of total local particle density is required. Here, we
discuss two definitions of local density in the context of many-body
dissipative particle dynamics. We show that only a potential which combines
local densities from all particle types in its argument gives physically
meaningful results for all composition ratios. Drawing on the ideas from metal
potentials, we redefine local density such that it can accommodate different
inter-type interactions despite the constraint to keep the main interaction
parameter constant, known as Warren's no-go theorem, and generalise the
many-body potential to heterogeneous systems. We then show via simulation how
liquid-liquid and liquid-solid coexistence can arise just by tuning the
interaction parameters.
