My honest advice? Don't. Mew2King is a very special player in a lot of ways, but look beyond him. You generally saw very little Melee/Brawl or Melee/4 overlap, and moreso than people only liking one game, it's just a time question I think. Playing a game competitively is a huge time investment, and I think most of us (myself included) that wish we'd place higher can mostly blame it on not putting in enough time to improve. If you do two games at once, you cut your time in half with each game on top of any messed up muscle memory or mental mistakes from trying to apply gameplay concepts from one game to another improperly.
IMO the best approach is to spend the first month or so of Ultimate giving it a really serious try, taking a vacation from Melee during that time, and then evaluate what you want to do from there based on how you feel about both games. Pick a game and make it your focus going forward. Maybe if you're still friends with the local scene for the other you enter events for fun on the side while you're focusing on your main game, but definitely you're best off having one main game that is the only game you're serious about improving at.