Begin by preheating your oven to 325°F (163°C).
Prepare three 8x2 inch round cake pans by greasing and flouring them thoroughly. For extra ease in releasing the cakes, line each pan with a round of parchment or wax paper.
In a mixing bowl, combine the cake mix, flour, and sugar, blending them for about 30 seconds to ensure even distribution.
In a separate bowl, whisk together the water, eggs, canola oil, and vanilla. Then add the peanut butter, mixing until smooth.
Add the wet mixture to the dry ingredients, blending on medium speed for 2 minutes. Pause after the first minute to scrape down the sides and bottom, then resume mixing for the remaining time.
Pour the batter evenly into your prepared pans. Place in the oven and bake at 325°F. Start checking for doneness at around 23 minutes; the cake should spring back slightly to the touch, and a toothpick inserted in the center should come out clean or with just a few crumbs. You may also notice the cake pulling away from the sides of the pan.
Baking at a lower temperature, 325°F instead of the usual 350°F, helps to reduce doming on the cakes for a more level surface.