Supposing that next year we get viable coldfusion and that em drive thing turns out to be actually real somehow it would seem feasible to move the planets, but how would you move the sun? You can't very well put an engine on the sun. Maybe a Dyson sphere, but that requires a lot of material, probably more than is available in our solar system, so we'd need to start significant extrasolar mining operations before we could move it.
Oh wow thanks, good to know there's a name for this idea with some amount of thought put into it. Might have to binge on cosmic megastructures reading.
I mean - crap - if you're doing going to do interstellar engineering, you might as well do it properly.