Abstract: Integrating topology optimization with additive manufacturing (AM) enables the generative design and fabrication of complex structures, offering great potential for high performance parts. However, the size and speed limitations of single-machine AM hinder its application in fabricating large-scale parts. Multi-machine collaborative additive manufacturing enables the fabrication of large-scale components beyond equipment size limits and enhances printing efficiency. This work proposes a topology optimization method for multi-component AM. In our work, the parametric level sets are utilized to describe structural components, and are combined with the density gradient to identify and control overhanging surfaces. The proposed method enables simultaneous optimization of structural layouts, components, and build directions, achieving support-free multi-component AM. Based on the parametric level sets, each component partition can be described using only a few parameters, and the component size can be explicitly controlled through the parameters of the level set function to fit the build size of manufacturing equipment. Numerical examples are presented to validate the effectiveness of the proposed method in simultaneous optimization of structural layouts, component partitions, and build directions for multi-component AM.