Play before a base score: deciding the order
From the rule book : http://www.alderac.com/smashup/files/2012/06/AEG-SU-Rulebook.pdf

Page 6


  Me First! If more than one player wants to use a Special  ability,
  start with the current player and go  around the table clockwise until
  all players pass in  sequence (if you pass and another player uses a 
  Special, you can then still choose to use a Special  of your own). If
  your Special allows you to play  extra cards, you must play those
  immediately or  not at all.


So each player may play one card until everyone is done.