To find the total amount of cheese made, you simply need to add the amount of cheddar cheese to the amount of Swiss cheese.
\[ 664.47 \text{ ounces (cheddar)} + 370.85 \text{ ounces (Swiss)} = 1035.32 \text{ ounces (total)} \]
Therefore, the cheese maker made a total of 1035.32 ounces of cheese.