When I lived with two cats (either Nutmeg & Coriander as coparent, or Mischief & Whiskers as baby sitter) the senior one (Nutmeg/Mischief) could not tolerate me petting the junior one at the same time. If I was petting the senior one first and the junior one wanted some of the action, the senior one would leave (in a huff, naturally); if I was petting the junior one and the senior one arrived, I would be totally ignored by Nutmeg ("You choose to pet this interloper, I ignore your miserable existence!") or stared at with disdain and loathing by Mischief. Never needed a third hand.