Q: If we are playing with mixed Trek Fluxxes, and more than one Transporter is in play, who gets what when Beam Us Up/Back! is played?

…and what about Attached Creepers?

A: First off, lets clarify that the people who can be Beamed Up (or Beamed Back) by any Transporter include all “Crew Members” (AKA “Starfleet Officers”) as well as the “Visitors and Other Personnel” called out by the DS9 version of this card.

OK, so we know that a standard transporter pad has six spots for people to stand on. (Never mind that some artwork seems to only show two spots, we know they can all handle six.) The person who plays Beam Us Up takes their choice of the first six eligible Keepers. Control then passes around to the next player in turn order who has a Transporter, that player beams up the next group of up to six. If any player has more than one Transporter in play, they get six per Transporter. This continues around the table, even possibly reaching the original player if there are enough eligible Keepers in play.

As for Creepers, any that are attached go with their crew members, and then are immediately replayed by the person who collected them, since Creepers cannot be in a player’s hand. See If someone plays Beam Us Up…