We present a method for fabricating general models with multi-directional 3D printing systems by printing different model regions along with different directions. The core of our method is a support-effective volume decomposition algorithm that minimizes the area of the regions with large overhangs. A beam-guided searching algorithm with manufacturing constraints determines the optimal volume decomposition, which is represented by a sequence of clipping planes. While current approaches require manually assembling separate components into a final model, our algorithm allows for directly printing the final model in a single pass. It can also be applied to models with loops and handles. A supplementary algorithm generates special supporting structures for models where supporting structures for large overhangs cannot be eliminated. We verify the effectiveness of our method using two hardware systems: a Cartesian-motion based system and an angular-motion based system. A variety of 3D models have been successfully fabricated on these systems.Note to Practitioner Abstract-In conventional planar-layer based 3D printing systems, supporting structures need to be added at the bottom of large overhanging regions to prevent material collapse. Supporting structures used in single-material 3D printing technologies have three major problems: being difficult to remove, introducing surface damage, and wasting material. This research introduces a method to improve 3D printing by adding rotation during the manufacturing process. To keep the hardware system relatively inexpensive, the hardware, called a multi-directional 3D printing system, only needs to provide unsynchronized rotations. In this system, models are subdivided into different regions, and then the regions are printed in different directions. We develop a general volume decomposition algorithm for effectively reducing the area that needs supporting structures. When supporting structures cannot be eliminated, we provide a supplementary algorithm for generating supports compatible with multi-directional 3D printing. Our method can speed up the process of 3D printing by saving time in producing and removing supports.