Below are some “semi-official” new selection variants for you to use in a campaign (or not!).
Eeny Meany
The oldest player draws a number of random aliens equal to one more than the number of players. That player assigns each other player one of the aliens. The youngest player decides which of the remaining two aliens to assign to the oldest player.
Democracy
Draw a random alien. On the count of three, all players point at any other player they want to assign that alien to. If a majority of players vote for the same player, they get the alien. If there is a tie, the alien is set aside and a new one is drawn. Repeat until all players have an alien except one. That player chooses one of the set-aside aliens if there are any, otherwise they draw one at random.
Try Your Luck
Deal out 2 aliens per player, half face up and half face down. Choose a player to go first, picking any alien, and continue counter-clockwise until all players have one alien. Whichever player chose last will be the first player when the game starts.
All-in All-the-time
Use only aliens that can be used as any player, any phase, randomly assigned.
White Elephant
The first player draws a random alien and adds it to their coalition. The next player clockwise can either steal an alien from any player’s coalition, or draw a random one and add it. Proceed until every player has the same number of aliens in their coalitions. When a player has had an alien stolen from them, they can either steal an alien from someone else (if it hasn’t been stolen since the last time a new alien was drawn), or else draw a random alien. Once a specific alien has been stolen three times, it cannot be stolen again. After the last player has added an alien to their coalition, the first player can choose to steal an alien from anyone, giving them one of their aliens in return.
Vote Bowl
Draw an alien for all to see. Players vote whether or not to add it to the alien pool. If a majority vote yes, set it aside. Otherwise discard it. Continue this until there are as many aliens in the pool as there are players. Then take the alien pool and deal it out randomly to the players.