It's not possible to do (at least , not as far as I know) but I like the idea personally , you could check the "New forum software" section and suggest it there If no one already did yet.
It's better to send PMs while quoting btw , that way you could go to your Outbox and see everything you sent while seeing what you received as well.
oh wow,cute little lifehack I didn't know of
it does make pm correspondence so much more convenient,having to switch from inbox to outbox to check the answers is annoying at times