Should I get a deeper cake pan or just get a third same size cake pan
Some recipes I'm looking at like this one
call for 3 layer cake, I only have 2 cake pans so I was thinking I found a cake pan in a store that is about 2x deeper than the cake pans I already have, I was thinking about letting it count as 2 cake layers and using my normal cake pan as the the 3rd layer. I was also thinking since I wanted to use a leches mix on it, I could pour tons of leche into the 2 for 1 cake layer and use it as a bottom and not worry about leches ruining the frosting as much.
When I lived in NYC I got many wonderful cooking items at Bridge Kitchenware. Once when I went to the counter to pay for three identical pans, Fred Bridge told me not to be ridiculous, that cake doesn't take that long to bake and that I should get only two pans and bake a third layer when the first two had been removed from the pans. Of course, I listened to him (I think that just about everyone always listened to him) and pass his sage advice along to you!
The baking instructions for three layers might not work perfectly well if you made one double-height layer and one regular layer. When cakes bake it takes time for the heat of the oven to penetrate the batter. If the batter is twice as deep it will take more time to bake it through and through. The extended baking time could make the outside overdone. So, to bake a layer that is twice as high/deep, you probably would need to bake it separately from the regular layer and lower the baking temperature and extend the baking time.
It would probably be easier and more reliable for you to get another cake pan to match the two you already have. Maybe you could borrow it from a friend.