Ok, after thinking about it for a while, I am thinking more and more of doing all custom cards. Most cards are going to be tweaked versions of existing cards to make balancing it somewhat manageable, but team-based cards don't have enough existing support to me. So it probably means I should take this project to a custom cards forum or something. Anyway, for the curious:
The cube is going to be structured around 4 color combinations. Each 4 color combo is going to have a theme, centered around one main color. The main color will have about 20 cards for the theme with the supporting colors having 5-10 cards. The goal is for many possible 2 color decks, with some 3 color decks possible. I want the overall power level to be somewhere between a peasant cube and an unpowered cube.
Two-headed giant is a lot different than 1v1. There are generally more creatures on the battlefield, more grindy games, more attacking/blocking, more creatures dying. Aggressive decks are worse in 2HG because one 2/4 can blank a team of 2/2s.
Anyway, the themes I'm thinking about are:
WUBR Rebels
UBRG Cycling
BRGW Sacrifice
RGWU Levelers
GWUB Counters
The first color is the main color with 20 cards in the theme, the other colors in the combination have 5-10 cards on theme.
Rebels are cool because they can be aggressive, but also grind out some advantage in the later game. WB Rebels was one of my favorite decks in Modern Masters 1, and it's an open, flexible theme. I'm basically going to "rebel-ize" a bunch of interesting creatures.
Cards like Astral Slide and Lightning Rift were powerful and cool. They are both pretty strong and a good template for doing other "cycling matters" type cards. I'm not totally sold on this theme though.
Sacrificing your own stuff is one of my favorite mechanics. It's been in a few sets, and looks cool in Battle for Zendikar. I'm not sold on this theme either.
Level Up was a cool mechanic that always seemed like it had more potential to me. Like Rebels, it lets smaller, more aggressive creatures do more in the late game.
+1/+1 counters are interesting, and abilities like graft are interesting in 2HG.
Aside from this, the rest of the cards in the cube are going to be creatures I wish existed for 2hg, like an Arbor Elf that can untap a teammate's land, etc.