re: 13 was the record! In march 1995
Between march 16 and 18, there was Soyuz TM21 arriving to Mir, Soyuz TM 20 staying and STS 67 leaving orbit for Earth.
Kondakova, Viktorenko, Polyakov, Strekalov, Dezhurov, Thagard, Lawrence, Jernigan, Oswald, Gregory, Grunsfelf, Parise, Durrance.
There was thus a crew change aboard Mir and a totally independant Shuttle flight with a crew of 7.
As today, all manned flights involve the space station, it's a record unlikely to be broken anytime soon.