The phrase "altogether different way" is correct and usable in written English.
It can be used to describe a method or approach that is completely distinct from others.
Example: "She decided to tackle the problem in an altogether different way, which led to innovative solutions."
Alternatives: "completely different manner" or "entirely distinct approach".
Rose's former husband continues to revolt, as do the staff kitchen in an altogether different way.
Bavaro, in contrast, arrived at tight end in an altogether different way.
After the Tunos, I was off to visit the Manochi family, which was happy in an altogether different way.
A snatched black-and-white portrait, starkly titled Divorce in Moscow, USSR, 1966, is powerful in an altogether different way.
There are piano arrangements of many orchestral works, but here a pianist stands in for an orchestra in an altogether different way.
Twenty-odd years later, after having acquired a good deal of experience with the opposite sex, not all pleasant by any means, I picked the book up again and found that I could appreciate it in an altogether different way.
Is there really an essentially English way of seeing and an altogether different Indian way of seeing, as Naipaul asserts in "Looking and Not Seeing: The Indian Way," the first of the book's two chapters on India, part reminiscence about his family's roots, part portrait of Gandhi?
"This kind of granular information will one day allow doctors to manage illness in an altogether different and precise way".
It's cathartic but in a different way altogether than shovelling snow, which, if you do it for pleasure as opposed to necessity, is kind of romantic.
The other approach — to make electric cars look altogether different — offers drivers a way to actively demonstrate an ecological commitment and a faith in new technology.
Imagine things a different way altogether.
