@nicksellen In my opinion you can do that. MIT is not copyleft, so it allows you to fork the project and put it under another licence. (Maybe there's a requirement about mentioning the former authors, but I'm not sure. Should be easy to find out.)
There could be patent issues though. The original copyright owners can sue you for patent infringement. (In contrast the Apache 2 licence says that the copyright owner will not sue you for that)
@nicksellen en.wikipedia.org says: "MIT licensed software can be re-licensed as GPL software [...]". But yes, I think it is good to check.
As I understand MIT allows basically everything including sublicencing. There's the condition to include the copyright notice and permission notice (Wikipedia says that disappears on relicencing). I see no reason that would withhold you from publishing your own contributions under AGPL. If they are substantial, that practically makes the full project AGPL.
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