How much do I have to change in order to claim copyright in someone else’s work?

Tricky. The usage needs to be transformative.

“Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create, a new version of that work. Accordingly, you cannot claim copyright to another’s work, no matter how much you change it, unless you have the owner’s consent. See Circular 14, Copyright Registration for Derivative Works.”
— U.S. Copyright Office