Only eight Frenchman have done the ultimate Audax double. Back in 1971, they finished PBP Audax in the afternoon and the next morning, they started (and finished) PBP Randonneur. Two PBPs in a week.
Since then, PBP Audax stayed on a five year schedule but PBP Randonneur shifted to every four years. In 1991, the PBPs were run simultaneously, so no chance to ride them back to back. In 2011, several folk rode both brevets but there was a fallow week in between.
In 2005, Richard Leon did Madrid-Gijon-Madrid 1200 and LEL back to back. I think there was a travel/ LEL registration day between them though. In 2009, John Evans did Gold Rush 1200, Super-Brevet Scandinavia 1200 and LEL in consecutive weeks. Impressive considering travel times, jet lag and riding a fixed wheel for all of them.
Not in the same league but some AUKs did a 400+ Easter Arrow and Buckingham Blinder 400 on successive days a while ago.