Jamie Brown died after being attacked along with two other teenagers in Ovenden on Saturday night.
West Yorkshire Police were called to reports that a teenage boy had been stabbed during a disturbance in East Park Road shortly before 9.30pm.
They found two boys with stab wounds and a third with a head injury.
A murder investigation was then launched by the Homicide and Major Enquiry Team (HMET) when Jamie died a short time later.
Six teenage boys are currently being held in custody as detectives continue to piece together the circumstances surrounding his death.
A police spokesman yesterday said: "Detectives arrested a further three males - aged 16,16 and 14 - on suspicion of murder overnight in connection with the incident in which Mr Brown received fatal stab wounds.
"Three 17-year-old males who were arrested on suspicion of murder on Saturday night also remain in custody."
Officers were seeking an extension to the usual custody time limits so that they could continue to question the suspects today.
Anyone who witnessed the incident or who has information is urged to contact police on 101, quoting log 1754 of 27 October.
Information can also be given via the live chat facility on the West Yorkshire Police website or by contacting the independent charity Crimestoppers anonymously on 0800 555 111.