The first of the four separate attacks happened on Monday, with the latest on Saturday afternoon.
The offences in Birmingham and Solihull are not linked, but have raised fears about knife crime in the area.
David Jamieson, the region's police and crime commissioner, said knife crime was a "major concern and has been for quite some time".
Timeline of attacks:
Mr Jamieson said: "There has been a growing trend that's particularly prevalent in the warmer weather, The warm weather does bring out more crime, particularly crime that happens on the streets.
"It's desperately worrying. Any increase in any violent crime is worrying.
"The police are there to tackle the violence so people will have the full weight of the law thrown at them."
Elsewhere, a 19-year-old man was arrested on Saturday in connection with a stabbing at Merry Hill shopping centre in Brierley Hill at about 11:15 BST.
A man was injured and taken to hospital for treatment.

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The Hoff has been seduced by the Scottish Premiership outfit during a Panto stint in Glasgow.
The former Baywatch and Knight Rider tweeted his support for the side earlier this month.
"They've been around since 1876 and I love that. It's about playing for themselves and playing for your honour," he told BBC Scotland.
Partick Thistle's new mascot Kingsley - designed by Turner Prize-nominated artist David Shrigley - caused a social media storm on its home debut in June.
The yellow character was paraded at Firhill Stadium, but The Hoff insists he is the club's new lucky mascot.
And he drew parallels with the side and one of his acting successes.
"It's like Knight Rider was a show about how one man can make a difference; you can make a difference in your own life and someone else's life," he said.
"That's what the team's about I think.
"We came over here [to Glasgow] and [were] making a joke about the worst team in the history of the world - if they win four games in a row then it's the best record in 40 years.
"There's something strange about that; it's a wonderful thing when you can come over and draw that energy. I am the lucky mascot and I'm proud to be the lucky mascot.
"I'm putting it out in a positive way and I'm the one who did all this. I said, 'let's give reference to Partick Thistle. I didn't know who they are? Let's find them'. We did.
"And that's what we do and I think that's why we've lasted so long and people respond to me. Knight Rider was real for me and when I got it I called my Dad and said, 'Dad, I've got the greatest show in the world'. I'm still living the dream."
Four men have died in a week of stabbings in the West Midlands.
[NEXT_CONCEPT]
American actor David Hasselhoff says he supports Partick Thistle because they are "a team for the people".