Public procurement mechanisms play a critical role in reducing drug costs and improving access to medicines. However, their competitive effects often fail to fully translate into private markets, where patient loyalty and physician preferences create quasi-monopolistic conditions for branded drugs. This paper proposes a novel mechanism that integrates public procurement and private market regulation. A branded-drug producer with market power competes with generic firms in a procurement auction, but it may opt out to retain unregulated monopoly profits. The optimal mechanism adjusts the allocation rule based on the firm's cost reports: For low-cost reports, it resembles a standard optimal auction. For high-cost reports, it favors the branded-drug producer in procurement while tightening price caps in the private market. This mechanism results in higher profits for all cost realizations, reflecting the role of higher informational rents driven by type-dependent outside option. Compared to standard practices, this mechanism yields significant welfare gains.