Does communis = co- + munus (and related words like communicare and communio), as though that which is shared/common "with" (co- < cum) involves a shared obligation/duty (munus)?
I'm thinking of how "companion" = cum + panis, in the sense that companions share/eat bread (panis) together/with (cum).
I don't see the word communis in de Vaan, Etymological Dictionary of Latin and the Other Italic Languages, perhaps because "communicate" seems to date from 3rd cent. in Tertullian (at least according to the OED).