Two females aged 18 and 16 and a 20-year-old man on the quad bike were confirmed to have died at the scene, between Upton and Hemsworth, West Yorkshire, and a second 20-year-old man was taken to hospital with critical injuries to his head and body.
He died on Sunday morning at Leeds General Infirmary, West Yorkshire Police said.
Officers were called at about 12.34am to a report of a collision between a bronze Nissan 350Z sports car and a quad bike on the A6201.
Two men aged 21 and 22, who were in the car, were arrested on suspicion of dangerous driving and remain in police custody.
Detective Chief Inspector Richard Holmes from the Homicide and Major Enquiry Team, who is leading the inquiry, said: "Widespread investigations are continuing into what is a significant incident on the district's roads which has now tragically resulted in the loss of four lives.
"Painstaking investigative work is continuing at the scene and the road itself will not be reopened until tomorrow. The victims are from the local area and are two men aged 20 and two females aged 18 and 16.
"Their families are currently being supported by specially trained officers and we are not in a position to release any further details of those who have lost their lives at this time."
He added: "We continue to appeal for witnesses to the collision and would also like to speak to anyone who may have seen a unregistered quad bike driven on the roads around the Hemsworth area in the evening of 26 September 2015 and up to 00.30 on 27 September 2015.
"Similarly I would appeal for any witnesses who saw a bronze-coloured Nissan 350Z driven in the Hemsworth area on the evening of 26 September 2015 and up to 00.30 on the 27 September 2015 to come forwards.
"Anyone who has information is asked to contact the Major Collision and Enquiry Team on 101."