Methods of additively manufacturing a part comprise dispensing a multi-part filament in three dimensions. The multi-part filament comprises an elongate filament body comprising a first body part extending longitudinally along the elongate filament body and comprising a first material that is configured to be cured responsive to a first cure condition, and a second body part extending longitudinally along the elongate filament body and comprising a second material that is configured to be cured responsive to a second cure condition that is different from the first cure condition. Methods also comprise concurrently with the dispensing, delivering curing energy corresponding to the first cure condition to impart a desired rigidity characteristic to the first body part to facilitate printing of self-supporting structures from the multi-part filament.