Sir Frank makes more frequent appearances in Yes, Prime Minister, and in doing so, appears as both an ally and competitor with Sir Humphrey. As allies, in the Yes, Prime Minister episode of "A Real Partnership," Sir Frank conspires with Sir Humphrey to push through a civil service pay increase in a time of financial stringency. As competitors, Sir Frank attempts to undermine Sir Humphrey by suggesting that he would be able to take Humphrey's role in heading half of the British Civil Service ("The Key"). Indeed, it is their roles as de facto joint heads of the Civil Service (Sir Humphrey as Cabinet Secretary and Sir Frank as Permanent Secretary of the Treasury) that brings them most often into conflict.
Both Sir Frank and Sir Humphrey share many things in common, not the least being an aim to increase Civil Service pay and prestige at the cost of others, an extraordinary command of the English language, fine dining, and a superb ability to manipulate and advance their own interests.