A system is disclosed for use in additively manufacturing a structure. The system may include a print head to discharge a material, and a support to move the print head during discharging to fabricate a structure. The system may also include a receiver mounted to the print head to generate a signal indicative of at least one of a shape, a size, and a location of the discharged material, and a processor in communication with the receiver and the support. The processor may be configured to generate a data cloud of the structure fabricated by the additive manufacturing system based on the signal and based on a known position of the receiver at a time of signal generation. The processor may also be configured to make a comparison of the data cloud and a virtual model of the structure during discharging, and to selectively affect discharging based on the comparison.