I think my game might just be bugged, I can't combine any of my thunderbirds, nor can I combine any cars I've lvled up (like my werewolf, Yurlungur, Ogre or Spriggan)... I can, however, combine my Pazuzu.
Edit: Apparently, if a card is over a specific level, the only way you can combine with it is if you do it through single card and not multiple cards. Apparently that also applies to all Thunderbirds...