As for your question, most PC computers are designed around one, or a limited number of microprocessors. This is true of both the sockets they must fit into, as well as the few or many supporting chips on any specific motherboard.
Even different "builds" of the same motherboard may not accept the same new chips after they are upgraded. Even experts in computer circuitry and design can need days to determine IF a change like you propose for any specific model is possible, or not.
It is possible to get an answer, but paying an expect to provide it would cost more than buying the newer chip in the proper motherboard it was designed for, even if the answer is, "no, it isn't possible."
This is what I expected.
From what I can tell, so far. My MB supports a dual core. I can get that chip for $15 on Ebay. I would however, like to know "FOR SURE" that it will work. I suppose $15 for trial and error is pretty cheap. But if I get the wrong "dual-core" for this trial/error, I'll end up spending the dollars on a new machine that I would otherwise not need to spend.
Thanks for your feedback.