  Sang, Shi and Yee, in 2020, found overpartition analogs of Andrews' results
involving parity in Rogers-Ramanujan-Gordon identities. Their result partially
answered an open question of Andrews'. The open question was to involve parity
in overpartition identities. We extend Sang, Shi, and Yee's work to arbitrary
moduli, and also provide a missing case in their identities. We also unify
proofs of Rogers-Ramanujan-Gordon identities for overpartitions due to Lovejoy
and Chen et.al.; Sang, Shi, and Yee's results; and ours. Although verification
type proofs are given for brevity, a construction of series as solutions of
functional equations between partition generating functions is sketched.
