National Security Challenge

How could Richard Nixon become Director of the FBI and RFK become Director of the CIA and serve simultaneously? In OTL Nixon was turned down in 1937 because the position was eliminated re budget cuts. The LA SAC recommended Nixon to Hoover, and he was willing to accept. JFK briefly discussed putting Bobby in the DCI chair instead of Dulles, but it would have shattered "plausible deniability." Bonus points for TL or one becoming POTUS.
 
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