If you google search "discontinuous constituent", you will see that various extensions to CFG have been proposed to describe discontinuous constituents. One of them is found in my favorite book on syntax, The Syntactic Phenomena of English by James McCawley, who begins his book with a proposed extension of CFG, since he is a proponent of discontinuous constituents, and gives many examples of discontinuous constituents in English in his book.
But my question is whether any extension to CFG is necessary. I have an answer to this question, "Not in some cases", which I will offer in due course.