Directed energy deposition (DED) for additive manufacturing applications is commonly realized by the usage of industrial robots. The DED processing end effectors are usually mounted on industrial robot systems and can, therefore, be moved and oriented in up to many degrees of freedom. However, the design of the powder nozzle and the programming of the robot can limit the movement options. For this reason, translational movements, as with conventional 3D printers, are still common today. The end effector is usually guided horizontal over the component surface although welding in position (PA) is preferred in general. It may be necessary to tilt the end effector in order to gain advantages during processing due to the constrained position. This is particularly advantageous for overhang structures and is often realized with the help of a turn-tilt positioning table in combination with an industrial robot. However, this approach is, in some cases, not possible due to geometrical constrains. To extend applications in this direction, advanced methods for slicing the components and programming the robot movements are necessary. The main aspect of this work is the development, testing, and evaluation of a multidimensional DED manufacturing approach. This is tested on a thin-walled component with defined overhang areas and compared with conventional approaches. Different strategies are assessed in terms of the geometrical match of the target geometry. Influences of strategies on the results are evaluated. It can be shown that multidimensional path planning approaches lead to a better match of the target geometry.