I need to make several layers for a cake. If I make the recipe as directed I will have more than my oven can handle at one time. Can I bake some then bake the others? Or will this cause my second baking batch not to rise or not turn out as well?

Your cakes will turn out fine. I refrigerate cake batter until I'm ready to use it all the time. Where I work we make about 10 gallons of cake batter at a time. Of course we don't need 10 gallons at a time. Anyway, your cakes will turn out the same as the ones that you bake first.

I have the same problem- not enough room. I also only have one pan for each size round, so I usually bake a couple rounds then refrigerate the remaining batter. Once the first batch has been baked and turned out on cooling racks, I wash the pans, fill em back up and put em in the oven. They always turn out fine.