Here is the format that I first thought Planechase would be like... then I read the rules and found out that I was wrong... so it's technically a homebrew of mine! Here goes.
Set up: Each player needs his or her own planar deck. You can do this by drafting decks, or having everyone build one at home (if they have the planes). They will need this deck to be shuffled, as well as whatever Magic Deck they want to play with. You will also need at least one Planar Die.
Playing: Invasion is a "flavour game". This means that if flavour says "no", you can't do it. What I mean by this is "Global effects" only have an affect on the plane that they happen on. There's no reason for an event on Mirrodin to effect Ravnica. Much the same, Planar effects and Chaos effects can only effect/target the player(s) on that plane. The same is true for target abilities from artifacts, creatures, enchantments or land. What does span across the planes? Instants, Sorceries, targeted abilities of Planeswalkers, and you can enchant an opponent's creature with an aura (This is more of the spell materializes on the creature, and not it materializes on your plane and moves over).
To attack a player, you must be on the same plane as that player. (again, it's a game of flavour)
This rule was made for Planar Collapse, but I liked it so much that I added it to a format I had made years prior. You may planeswalk for free by forefitting your turn. This means that after the opponent before you ends his or her turn, and before your untap step, you may say "I'm going to planeswalk." You then planeswalk however you'd like. Because you don't have a turn, this technically gets around "When you planeswalk away from ..." abilities on some planes, like Norn's Dominion... You also lose out on the "When you planeswalk to ___, do stuff." abilities. When you planeswalk, all of your stuff comes with you. (That question comes up sometimes)
When you planeswalk, you have two options. A) Put the current plane that you are on, on the bottom of your planar deck and reveal the next plane on your planar deck. B) Move to somebody else's plane. When you do this, you'll be able to attack and do everything that you normally could.
If you are on another player's plane, they can planeswalk away from you, to another player's plane (they are going to be stuck with a buddy for a while). If they chose to, they can planeswalk away from the plane that you two are both on, and put that plane on the bottom of their planar deck, revealing the next plane. You both planeswalk to that plane (because you're chasing them!). (it's times like this that Norn's Dominion aren't so shabby.)
The winner is the last player standing.