- March 1995, STS-67 (7), Mir (3), Soyuz TM-21 (3)
- February 1997, STS-82 (7), Mir (3), Soyuz TM-25 (3)
- July 2009, STS-127 (7), ISS Expedition 20 (6)
- March 2010, STS-131 (7), ISS Expedition 23 (6)
At the moment, it peaks at nine (one ISS expedition plus one visiting Soyuz). When the US commercial-crew vehicles start flying, I assume they will be timed so that there is not a Soyuz and US crew rotation flight at the same time - it would seem to make things very complicated - and that will keep the peak at nine.
A Shenzhou flight at the same time as crew rotation would bring the total to twelve.
With what we know about future plans, is there any plausible combination of missions likely to fly in the next few years that would set a new record at fourteen?