I think I've brewed five batches in one weekend (3 Saturday, 2 Sunday) a few times when in NHC mode. Don't recall the batch sizes; probably 5, but some could have been 10. Both fit on my system, and it's not much extra work/time. Depends on how much I need. One batch takes about 5 hours; each additional batch adds about 2 hours. Better have all your supplies stored up, especially propane and water...
Don't remember if there was racking/packaging going on at the same time. I often do keg maintenance and other random beer things while brewing, although when I stack up batches like this, I'm usually prepping the next batch while brewing the current batch.