Additive manufacturing in the field of regenerative medicine aims to fabricate organized tissue-equivalents. However, the control over shape and composition of biofabricated constructs is still a challenge and needs to be improved. The current research aims to improve shape, by converging a number of biocompatible, quality construction materials into a single three-dimensional fiber deposition process. To demonstrate this, several models of complex anatomically shaped constructs were fabricated by combined deposition of poly(vinyl alcohol), poly(ε-caprolactone), gelatin methacrylamide/gellan gum and alginate hydrogel. Sacrificial components were co-deposited as temporary support for overhang geometries and were removed after fabrication by immersion in aqueous solutions. Embedding of chondrocytes in the gelatin methacrylamide/gellan component demonstrated that the fabrication and the sacrificing procedure did not affect cell viability. Further, it was shown that anatomically shaped constructs can be successfully fabricated, yielding advanced porous thermoplastic polymer scaffolds, layered porous hydrogel constructs, as well as reinforced cell-laden hydrogel structures. In conclusion, anatomically shaped tissue constructs of clinically relevant sizes can be generated when employing multiple building and sacrificial materials in a single biofabrication session. The current techniques offer improved control over both internal and external construct architecture underscoring its potential to generate customized implants for human tissue regeneration.