An additive manufacturing system is disclosed. The additive manufacturing system may include a matrix reservoir, a primary nozzle fluidly connected to the matrix reservoir, and a primary cure enhancer operatively connected to at least one of the matrix reservoir and the primary nozzle. The primary cure enhancer may be configured to direct a cure energy toward a tip of the primary nozzle. The additive manufacturing system may also include an auxiliary nozzle, an arm configured to mount the auxiliary nozzle at a trailing side of the primary nozzle, and a passage extending from the matrix reservoir to the auxiliary nozzle.