Do significant changes to code allow a license change from 3-BSD to something else?

Question

Suppose person X writes some library foolib, licensing it under the 3-BSD license.

Person Y now takes the foolib sources and develops it further, making significant changes: More functionality, changes to existing API, partial rewrite of the internals etc.. But of course, it is still an evolved and changed foolib.

Can person Y release their modified library under another license? e.g. GPL or LGPL? If so, what is the threshold to the amount of change necessary so that the original 3-BSD license doesn't "stick" to it, and its legal use is restricted to the terms

Notes:

• Not a dupe of the Theseus paradox question, as that one doesn't address whether I can distribute a derivative work under a different license.
• Other related questions:
  • Relicense BSD 2/3-clause code to GPL
  • Can I take BSD licensed code and distribute it under GPL?
• If it matters whether the library is source-only or object+headers, please mention this. Also if other aspects of the programming language matter.