This probably won’t work, but do we care? No.
So, there’s a variety of rules for Commander cubes. In some cases you draft your commander separately, but here, since there’s so many potential brawlers in the format, there’s no need to go there. You just have to remember to draft a commander early. The problem is that if you happen to sit next to someone with the same colors, you’ll be both in a very poor situation, which means that reading signals becomes of utter importance. In order to minimize this, I would suggest using more than three packs per player. Also, since there’s several very powerful colorless cards, we could maybe think about having more than one of each in the cube, but for now, I’ll put in only one.
The idea here is to play conspiracy style, meaning each player sits in the same draft, but after deckbuilding they are divided into two groups of four for games. You might consider drafting through another method, such as Rochester. You might also consider having smaller than 60 card decks. 40 or 50 would probably work better. It would probably be a good idea to make sure there’s enough, maybe all, potential commanders in the first pack.
There’s currently 1639 legal cards in standard. Supposing we play with four boosters for each player, that’s a 480 card cube. With 67 lands, of which we’ll play, say, 40 (but could easily fit more, as I’m leaving quite a few good options out), and with 178 colorless artifacts, of which we’ll also use 40, and 144 multicolored cards (including Aftermath), of which we’ll use 100 (which is quite a few, but these are generally more powerful and include quite a few potential commanders), this leaves us room for 300 monocolored cards or 60 for each color. This does mean that monocolored commanders are going to be pretty hard to pull off, although there is going to be some artifacts with a color identity. Maybe there should be more artifacts for this reason. I’ll leave out all the three colored commanders, because I don’t think the manabases can handle them.