  We show that it is possible to formulate the most general first-class gauge
algebra of the operator formalism by only using BRST-invariant constraints. In
particular, we extend a previous construction for irreducible gauge algebras to
the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd,
mutually anticommuting BRST operators that bear structural similarities with
BRST/anti-BRST theories but with shifted ghost number assignments. In both
cases we show how the extended BRST algebra can be encoded into an operator
master equation. A unitarizing Hamiltonian that respects the two BRST
symmetries is constructed with the help of a gauge-fixing Boson. Abelian
reducible theories are shown explicitly in full detail, while non-Abelian
theories are worked out for the lowest reducibility stages and ghost momentum
ranks.
