The latest murder probe was launched last Friday after Jordan Marples-Douglas, aged 23, was stabbed in a house on Woodthorpe Road, Woodthorpe.
Two arrests have been made over the killing.
Another 10 case are still being worked on, including the death of a nine-week old baby, a two-year-old boy and a mum-of-four.
Anyone with information about any of the deaths should call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.
Another 10 case are still being worked on, including the death of a nine-week old baby, a two-year-old boy and a mum-of-four.
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