A 17-year-old and two 18-year-olds have been arrested on suspicion of following the death of Thomas Taylor, 17, who was near a in on Wednesday, Bedfordshire Police said.
The force detailed that the individuals were arrested on Friday.
A fourth person, a man in his 60s, was arrested on suspicion of assisting an offender on Thursday and has been bailed pending further inquiries, PA reports.
Thomas was attacked in Greenhill Street, Bedford, at around 5.50pm on Wednesday.
Detective Inspector Richard Stott is leading the investigation for the major crime unit.
He said: "This is an absolutely shocking incident in which a teenage boy has lost his life as a result of knife crime and serious youth violence.
"We want to reassure the wider community that officers are pursuing all lines of inquiry as well as carrying out increased patrols in the surrounding area.
"We are continuing to appeal for anyone who was in the area at the time and may have witnessed the incident, or the lead up to it.
"We are also keen to speak to anyone who knows those involved, and we would encourage you to make contact with us via the ."
Thomas' mother has said that her son had a "beautiful soul" and the family was "proud of the young man he was becoming", the reports.
Samantha Taylor added: "He was really looking forward to his future and we are all completely devastated."
She also said: "He was deeply caring and family orientated and was a very intelligent boy.
"He brightened up any room he walked into he really cared about others and his life."
Police have urged the public, if have any information which could help with their investigation, to contact them on 101 or online quoting Operation Cimarron.
The public can also provide information anonymously, via the or via Crimestoppers, on 0800 555 111.