Light-initiated additive manufacturing techniques typically rely on layer-by-layer addition or continuous extraction of polymers formed via nonliving, free radical polymerization methods that render the final materials "dead" toward further monomer insertion; the polymer chains within the materials cannot be reactivated to induce chain extension. An alternative "living additive manufacturing" strategy would involve the use of photocontrolled living radical polymerization to spatiotemporally insert monomers into dormant "parent" materials to generate more complex and diversely functionalized "daughter" materials. Here, we demonstrate a proof-of-concept study of living additive manufacturing using end-linked polymer gels embedded with trithiocarbonate iniferters that can be activated by photoinduced single-electron transfer from an organic photoredox catalyst in solution. This system enables the synthesis of a wide range of chemically and mechanically differentiated daughter gels from a single type of parent gel via light-controlled modification of the parent's average composition, strand length, and/or cross-linking density. Daughter gels that are softer than their parent, stiffer than their parent, larger but with the same modulus as their parent, thermally responsive, polarity responsive, healable, and weldable are all realized.