I recall this was done in another discussion not long ago.
The Liverpool Street-Kings Lynn route has 5 stations with staggered platforms: Roydon, Harlow Mill, Elsenham, Waterbeach and Watlington. All have, or used to have, a level crossing between the platforms. Watlington is an interesting example because it originally had standard opposite platforms.
The pre 2012 Cambridge layout with one long through platform and a central scissors crossing could also be described as "one platform starts where the other ends".
Bishops Stortford is almost completely staggered with only a short overlap. Audley End and Great Chesterford are also partially staggered.