Whether one uses an animal for an additonal offering or for the Daily Offering, where there aren't enough for both: Menachot 49a-b
The Above, where the choice is between an additional offering and the Daily Offering for the next day: Menachot 49a
The bringing of Additional Offerings suspends Special Prayers of the Shifts of National Representatives: Taanit 26a, 28a-b
The bringing of the Additional Offerings is for forgiveness for Impurity in the Temple and its Offerings: Rosh HaShanah 4b