We present Zone and Polygon menus, two new variants of multi-stroke marking menus that consider both the relative position and orientation of strokes. Our menus are designed to increase menu breadth over the 8 item limit of status quo orientation-based marking menus. An experiment shows that Zone and Polygon menus can successfully increase breadth by a factor of 2 or more over orientation-based marking menus, while maintaining high selection speed and accuracy. We also discuss hybrid techniques that may further increase menu breadth and performance. Our techniques offer UI designers new options for balancing menu breadth and depth against selection speed and accuracy.