You can use the flex-edge beater attachment to mix at the edge of the bowl.
Brad's Deals Editor Jim,
This KitchenAid Artisan 5-Quart Tilt-Head Mixer with Flex-Edge Beater lists at $499.99, but you can get it for $229.99 during this sale at Macys.com. Shipping is free. That's the best price we can find anywhere by about $50 for this set, which includes a flex-edge beater attachment. It also comes with a flat beater, dough hook, and wire whip. Choose from two colors. Sales tax is charged in most states.