4D printing magneto-responsive shape memory polymers (SMPs) using biodegradable nanocomposites can overcome their low toughness and thermal resistance, and produce smart materials that can be controlled remotely without contact. This study presented the development of 3D/4D printable nanocomposites based on poly (lactic acid) (PLA)-poly (butylene adipate-co-terephthalate) (PBAT) blends and magnetite (Fe3O4) nanoparticles. The nanocomposites are prepared by melt mixing PLA-PBAT blends with different Fe3O4 contents (10, 15, and 20 wt%) and extruded into granules for material extrusion 3D printing. The morphology, dynamic mechanical thermal analysis (DMTA), mechanical properties, and shape memory behavior of the nanocomposites are investigated. The results indicated that the Fe3O4 nanoparticles are preferentially distributed in the PBAT phases, enhancing the storage modulus, thermal stability, strength, elongation, toughness, shape fixity, and recovery of the nanocomposites. The optimal Fe3O4 loading is found to be 10 wt%, as higher loadings led to nanoparticle agglomeration and reduced performance. The nanocomposites also exhibited fast shape memory response under thermal and magnetic activation due to the presence of Fe3O4 nanoparticles. The 3D/4D printable nanocomposites demonstrated multifunctional multi-trigger shape-memory capabilities and potential applications in contactless and safe actuation.