After watching a movie about criminal masterminds, Penguin is inspired and forms Team Penguin by gaining powerful criminals around Gotham City as well as recruiting newcomer; Killer Moth, who later becomes the most powerful member with his new abilities and powers. Their plans was to finally eliminate Batman as well as become rich. Their plans were foiled though after Batman, Robin and Batgirl defeated them and sent them back to Arkham Asylum.
Penguin did sent invitations to Joker , Mr. Freeze and Riddler but the three said no to the offer. And he sent one to Bane too but he was taken down by Robin and Batgirl before he even could make a choice.