I have got a general question. I am sure this is possible. I am trying to use a function that is similar to the SUMIF & COUNTIF functions, but I want it to go one more level...example

---A--B--C
1 cat 2 1
2 dog 3 4
3 cat 3 2
4 cat 2 2
5 dog 3 2
6 cat 1 3
7 dog 5 4
8 cat 2 2
9 cat 5 2

If I am trying to sum column C that meet the criteria - Column A = "cat" and Column B = "2"...I know that if I wanted to sum Column B for cats, I could "=SUMIF(A:A, "cat", B:B)"...but how do I do one more level to sum if it meets two criteria?