A system for additively manufacturing an object comprises a fiber supply that dispenses elongate fibers, a resin supply that applies a resin to the elongate fibers to create a feedstock line with the resin in a first non-rigid uncured state, a rigidizing mechanism that transforms the resin from the first non-rigid uncured state to a rigid uncured state, a delivery guide that deposits the feedstock line along a print path, a feed mechanism that feeds the feedstock line through the delivery guide, a de-rigidizing mechanism that transforms the resin from the rigid uncured state to a second non-rigid uncured state, and a curing mechanism that transforms the resin from the second non-rigid uncured state to an at least partially cured state.