Four men were arrested on Friday, bringing the total now under investigation to 14.
The men, aged between 22 and 34, were arrested for offences including rape, sexual assault, conspiracy to rape and conspiracy to commit human trafficking.
All four, who are from the Cleveland area, have since been released under investigation.
The arrests came after officers arrested 10 other men in a series of coordinated raids earlier this month.
A 30-year-old man was arrested on suspicion of rape at an address in Callow Mount, Gleadless Valley, and later released under investigation after questioning.
Detective Inspector Chris Stone, leading the investigation, said: "Progress continues to be made with the support of our communities to target those who seek to exploit vulnerable people. Arrests continue to be made, properties searched and evidence gathered."