In 2009, HK rode the Gold Rush 1200, Madrid-Gijon-Madrid 1200 and London-Edinburgh-London 1400 at two-week intervals. John Evans added the Super-Brevet Scandinavia 1200 between MGM and LEL.
Provided you get enough sleep (between and during both PBPs) and don't over-exert yourselves during the first PBP (the Audax format assists in this aim), you'll be fine. HK and I rode an overnight UAF 400 the weekend after finishing the Texas 1200 a few weeks ago with no major problems, though more sleep would have been appreciated.
FWIW, HK and I have signed up for the early August session, as will most of the Anglophone PBP Audax entrants. We've also signed up for the 84 hr PBP Randonneur.