Is there anything I can add to/change about a store bought white or yellow cake mix to take it from ordinary to extraordinary?
There are a couple of cookbooks by Anne Byrn who has built a franchise on this subject. Her best known book (and the one I have) is titled The Cake Mix Doctor. written specifically on this subject.
Go to her website http://www.cakemixdoctor.com as there are several recipes and articles as well a listing of her books.
Using different spices, maybe a pumpkin pie spice added to vanilla cake, will give your cake a completely new and interesting flavor. Using citrus zests will spice things up as well! I have also used different flavored liquid extracts, added these to icing can really add that extra something special to the completed cake.
Substitute part of the butter with creme fraiche - say, 2oz creme fraiche for 1oz of the butter.
All answers provide great ideas but I'll take Jginger's spice recommendation a step further. I often use what I call "subtle exotic" spice combinations which is simply a fancy way of saying unusual or ethnic-influenced combinations. For example, Black pepper with dark chocolate; chili pepper and cinnamon; or cardamom. These types of spice combinations aren't typical in a cake and will provide a deliciously memorable flavor for your guests. A recent unusual combination I just tasted was a spiced gin cupcake. The baker used a basic cake recipe then infused spices and gin into the batter and frosting. A boxed cake could be that basic recipe.
When I make box cake mixes, I use vanilla almond milk instead of water and olive oil instead of vegetable oil. The vanilla almond milk gives it a hint of sweetness and the olive oil makes it fluffier. And then a add a touch of cinnamon and nutmeg.