While algorithmic systems have become widely used for many impactful socioeconomic determinations, these algorithms are unique to their circumstances. This challenge warrants an approach to governing algorithms that comprehensively enables application-specific oversight. To address this challenge, this paper proposes granting two new authorities for key regulatory agencies: (1) administrative subpoena authority for algorithmic investigations, and (2) rulemaking authority for especially impactful algorithms within federal agencies’ existing regulatory purview. This approach requires the creation of a new regulatory instrument, introduced here as the Critical Algorithmic Systems Classification, or CASC. The CASC enables a comprehensive approach to developing application-specific rules for algorithmic systems and, in doing so, maintains longstanding consumer and civil rights protections without necessitating a parallel oversight regime for algorithmic systems.