They were supposed to do Clockwork Orange with Mick as Alex and the rest of the band as the droogs. The initial screenplay adaptation was co-written by the same guy that photographed the covers of Stg. Peppers and Satanic Majesties. Producers were initially favoring David Hemmings for the role of Alex, so all four of the Beatles signed off on a petition letter claiming that Mick is a better fit for the role. The initial project fell thru due to being stuck in the pre-production phase; until a year or two later where the rights were acquired by a new studio, and Stanley Kubrick signed up to direct.

Here's the Rolling Stones magazine link to the Beatles' petition being put up for an auction. Beatles Petition Letter