In fact, you can. See, for example ACE model, which explicitly attempts to separate generic causation from shared environment and from non-shared environment. This can be done using twin studies, by comparing correlations between monozygotic vs dizygotic twins on various variables of interest, see Falconer’s formula for example.

This research is not new, it has been done for many decades now. The word “heritability” has a well established technical meaning.