If a project is licensed with MIT license, can someone fork the project, create significant changes, and put a more restrictive license on it? Or even copyright it?
So we suppose that Alice creates a piece of code ab initio and publishes it under the X11 licence (the more precise name of what is often referred to as "the MIT licence"). Bob then copies it and makes significant changes (resulting in the new work).
Can Bob copyright it?
The new work is a piece of code in which two people, Bob and Alice, have a copyright interest. That's not something either of them has to do, it flows out of their authorship and the Berne Convention. No third party may then do with the new work those things which are restricted by copyright without the consent of both Alice and Bob; Alice and Bob may each do only those things with the consent of Bob and Alice, respectively.
By publishing under a non-copyleft free licence, Alice has permitted a very wide range of things to be done.
Can Bob put a more restrictive licence on it?
As I have written elsewhere, yes, he may. Some free software licences forbid distribution under terms more restrictive than their own (eg GPLv3 ss 5c, 7); the X11 licence is not one of these. Bob may therefore distribute the new work under the requirements of both the X11 licence and (eg) GPLv3. Note that this isn't dual-licensing, where the recipient chooses which of two licences (s)he wishes to apply; the requirements of both licences apply. GPLv3 permits this since the demands of the X11 licence do not conflict with those of GPLv3 (ie, X11 is "compatible" with GPLv3); X11 permits it since it does not forbid adding additional restrictions.
Bob may even distribute the new work under almost-completely-restrictive terms, as proprietary software, so long as he fulfils the (very lightweight) labelling requirements of the X11 licence.