Bressoud style identities for regular partitions and overpartitions

We construct a family of partition identities which contain the following identities: Rogers–Ramanujan–Gordon identities, Bressoud's even moduli generalization of them, and their counterparts for overpartitions due to Lovejoy et al. and Chen et al. We obtain unusual companion identities to known theorems as well as to the new ones in the process. The proof is, against tradition, constructive and open to automation.