A 19-year-old man from Walsall was arrested on suspicion of murder on Thursday.
Meanwhile, a 24-year-old man, from the Wednesbury area, was also arrested on suspicion of assisting an offender.
West Midlands Police confirmed on Wednesday that they had also arrested a 23-year-old man from the Tipton area on suspicion of murder, while a 21-year-old man, was arrested in London later that afternoon.
The two men arrested on Wednesday remain in custody.
Kimani was a passenger in the private hire vehicle when a shotgun was fired at it from a dark hatchback on Dudley Road East.
The car then sped away from the scene of the shooting, which happened just before 1.30am on Sunday, June 20. Three special constables who were nearby came across the scene and tended to the youngster, but nothing could be done to save him.
He was taken to hospital and pronounced dead a short time later.
Anyone with information is asked to call West Midlands Police on 101, quoting crime number 20/1126386/21.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org