The most serious sex attack happened between 2am and 4.40am on August 27 at the junction of Chapeltown Road and Grange Avenue.
A 16-year-old girl was subjected to "a serious sexual assaulted", a spokesman for West Yorkshire Police said.
It came just one day after a 19-year-old woman was grabbed, and forcibly kissed, at the same location at about 8.30pm.
The teenager had been celebrating the carnival weekend with friends when the offender struck.
Police today (Monday) issued an E-Fit image of the man they are trying to trace in connection with the offences.
He has been described as being as black, aged 30 to 40-years-old, about 6ft tall and had a short beard.
The man was wearing a white and black sports-style jacket.
Anyone with information is asked to call police on 101, quoting crime reference 13180426842.