The phrase "altogether different subject" is correct and usable in written English.
It can be used when indicating that a topic being discussed is completely separate from another topic.
Example: "While we were discussing climate change, the impact of social media on mental health is an altogether different subject."
Alternatives: "completely different topic" or "entirely separate matter".
But Mr. Cheney is an altogether different case.
Given the current state of popular opinion, he might understandably wish to choose a different subject altogether.
Cultures mysterious and intriguing for altogether different reasons are the subject of "Shadows in the Forest," on Nickelodeon this afternoon at 5 45, an entry in the National Geographic "Explorer" series.
(A more progressive tax rate would be a good second, but that's a different subject altogether).
In this way "Simon" reminded me of Ian Hamilton's "In Search of J. D. Salinger," which similarly sets out to be a biography but ends up, under relentless pressure from its subject, an altogether different kind of book, about the challenge of capturing an unwilling living figure in a dead paper medium.
Woods has been subject to an altogether different reaction.
On the other hand, a determination whether the permissible use of a specific piece of property should be changed is usually an exercise of judicial authority and its propriety is subject to an altogether different test". Fasano v. Board of County Comm'rs, 264 Or. 574, 580-581, 507 P.26 23, 26 (1973).
The experience of teaching the subject of Israel Palestine at Riverdale is, in certain crucial respects, altogether different than the experience of teaching any other subject.
Those who attack that role have an altogether different agenda, and that too should be the subject of legitimate public questioning and exposure.
Yet anyone who explores the subject on the Internet quickly discovers an altogether different side of autism.
The case before us is altogether different.
