I actually owned a Bruheat = Electrim boiler in the late 70s when I lived in Cardiff and used it as a 2 vessel system (the other vessel just being a bucket style white fermenter) - I used to mash in it, in the premade bags you can still get to fit it, then drain into the second vessel, sparge using hot tap water into the second vessel, then when I had enough wort I would remove the bag and pour the wort back in, then boil. Never had any problems and I used to do it in a bedsit with steam pouring out through the window, amazing I never got raided
Looking back, the bag was merely for convenience in removing the grain, we didn't make the "connection" and use it as a true BIAB system.
As RdeV says you could do a thicker mash, one sparge, a boil and dilute post boil to give you a 23L length.
