The question ''To which states can bosons crowd?'' has the only possible answer ''to a boson condensate''. This is a family of collective states of the bosons, determined (if they form) collectively by the interactions and the temperature.
The internal composition of a boson (elementary or composed of constituents, e.g., fermions, as in the case of He-4) is irrelevant for the problem of boson condensation. When one talks of boson condensation, one already chose to ignore the substructure and replaced it by a bosonic model with effective interactions. These residual interactions are of ''usual'' sizes, so the density resulting is also ''usual''.