A system is disclosed for use in additively manufacturing a structure. The system may include an additive manufacturing machine, a memory having computer-executable instructions stored thereon, and a processor. The processor may be configured to execute the computer-executable instructions to determine if a tool path to be followed by the additive manufacturing machine during manufacture of the structure is located in free-space or on top of another tool path. When the tool path is located in free-space, the processor may be further configured to execute the computer-executable instructions to make a determination regarding a curvature of the tool path, and to selectively cause the additive manufacturing machine to fabricate a support for the tool path based on the determination.