The trio, all in their 20s, were taken to hospital after being knifed in the Carver Street area in the early hours of Saturday.
Three men, aged 27, 19 and 26 were arrested on suspicion of wounding and violent disorder. The older man remains in custody and the other two have been bailed, the force said.
The information updates an earlier appeal for witnesses and comes after emergency services were called to reports a man had been stabbed and a second run over.
Police were treating the incidents as linked. Carver Street and Rockingham Street were closed while officers carried out investigations.
Det Insp Mark Cockayne, investigating, said: “Enquiries are continuing at pace and I am keen to hear from anyone who may have witnessed the incident to please come forward. I am particularly keen to speak to people who may have captured the incident on their mobile phones.
“There will continue to be a heightened police presence in the area as officers continue their work and to provide reassurance. Please speak to them if you have any concerns or any information which could help the investigation – they are there for you.”
On Saturday, police also said a man was arrested on suspicion of possession of controlled drugs with intent to supply.
Anyone with information which could help officers should call 101 quoting incident number 196 of 9 September. Or contact Crimestoppers anonymously on 0800 555 111 or at www.crimestoppers-uk.org