A man alleged to have been driving the car involved has been charged with two counts of causing serious injury by dangerous driving after the crash happened in south west Birmingham on Sunday.
The Mercedes A-Class AMG involved is believed to have been driving "in tandem" with a VW Golf shortly before it left Woodgate Lane, near Junction 3 of the M5 in Bartley Green, and hit the bus stop at around 9pm.
One passenger in the car, aged 22, is understood to have suffered permanent spinal cord damage and remains in hospital, West Midlands Police said.
A second passenger, 19, suffered leg and pelvis fractures and a third suffered minor injuries.
One of the men was thrown out of the car when the crash happened and another had to be cut free by firefighters.
Jordan Tedstone, 22, from Cartmel Grove, Bartley Green, is accused of driving the car and has been remanded in custody after appearing at Birmingham Magistrates Court on Wednesday.
West Midlands Police officers want to hear from anyone who saw the crash or the white Mercedes travelling in the Bartley Green area before the collision.
Sergeant Mark Crozier from the Serious Collision Investigation Unit, said: “We believe the car was travelling in tandem with a white VW Golf shortly before the collision. We’ve spoken to that driver and he’s helping us with our enquiries.
“I really need to speak to anyone who was in the Bartley Green area at the time and saw the two cars – or any other motorists that may have caught the vehicles on dash-cam footage.
“We need to build-up a clear picture of what happened in the build-up to the collision.”
Anyone with information is asked to contact police quoting log number 3892 from June 13.