The Incense of the Princes of each tribe in the desert was brought on the External Altar as a matter of special dispensation: Menachot 50a
Allowed a rape victim to marry a Kohen if the rapist had unknown lineage: Ketuvot 14b
Allowed those who returned to Israel from Bavel for the second Temple, to bring offerings atoning for intentional idolatry: Temurah 15b
