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 cause the additive manufacturing machine to discharge a path of composite material, and to make a determination regarding existence of support located at a side of the path of composite material. The processor may be further configured to execute the computer-executable instructions to selectively cause the additive manufacturing machine to compact the path of composite material after discharge with a variable pressure that is based on the determination.