The CIA is a mystery cult. Not explicitly, of course, but its organization of successive inner circles possessing increasingly more important secrets mimics the form perfectly. There are even "initiation rites", designed to test candidates for their ability to keep secrets, commonly including gaslighting, imprisonment, interrogations, and even false executions.
The uninitiated maintain mundane intelligence analysis duties. This is the public face of the agency, doing the sorts of work an intelligence agency is expected to do. Their primary concern is suppressing dissidents at home while supporting them abroad, especially in the USSR.
Members of the agency-within-the-agency are self-selected. Especially talented analysts, who, noticing the ways in which official narratives are insufficient, go hunting for their own explanations, and, crucially, find them. These people must be either initiated or killed. This inner circle is concerned with the secret war against the deep ones, know of the Elder Things held by the USSR, and have suspicions about the existence of the Mi-go. They have transcripts of Soviet/Elder Thing interviews, shoggoth samples, and numerous uncategorized anomalies.
The agency goes one level deeper. Inside the inner circle are the true masters, a group of transplants, seeking a Yithian archive, from which they can learn the true and secret history of the world.