Police have been searching for Lee Martin since the 41-year-old fled when officers went to arrest him last week.
He was initially due to be detained on suspicion of kidnapping, beating and stabbing a woman in Solihull.
But since the incident September 5 the force believes he has stolen a car, committed a burglary and carried out two knifepoint carjackings across Birmingham.
Police suspect he also rammed traffic officers to escape and have warned the public he is "possibly armed and very dangerous" and they should call 999 if they see him.
Superintendent Darren Walsh said: "All police forces in the country have been told that Lee Martin is wanted but we strongly suspect that he is still hiding out somewhere in Birmingham.
"In all of the crimes that he is suspected of carrying out, knives have been used meaning Lee Martin is possibly armed and very dangerous. That’s why we’re asking you to dial 999 if you see him."
Police suspect the 41-year-old stole a black BMW from a woman in Kings Heath Park. The car was found two days later on nearby Branscombe Close.
Meanwhile CCTV from Asda in Barnes Hill shows a man, who the force believes is Martin, stealing a woman’s grey Nissan Qashiqa at lunchtime on Friday. The woman was threatened with a knife and attacked before her car was stolen. The car has since been found and is being examined by forensic specialists.
Four hours later, a house was broken into on Stonebrook Way, Harborne. The householder disturbed the burglar who had a knife and is believed to have been Martin.
Then at 7.45pm on Saturday, a navy blue Corsa was stolen at knifepoint from a woman who had dropped her daughter at university.
The car, which was stolen in Lionel Street in Birmingham city centre, is yet to be recovered.
The charity Crimestoppers in offering a reward of up to £3,000 for any information that leads to the arrest of Martin. People who see Lee Martin should avoid him and instead call police on 999.
Anyone who has any information about where be may be hiding out or anything else which may help, call Crimestoppers on 0800 555 111