Imho they have everything that they taped along their career. That might start with the 1969 American tour tapes plus the Saville Theatre late 69 gigs.
Unlike Led zep (where live tapes have gone missing soemtime in the 80's) or Dylan (who lost chunks of live archives : the tapes from his 78 tour have all been erased) the Stones have preserved everything.
What lacks though is the will to exploit and release this archival treasure!