Thermo-sensitive shape-memory polymers (SMP), which are capable of memorizing two or more different shapes, have generated significant research and technological interest. A triple-shape effect (TSE) of SMP can be activated e.g. by increasing the environmental temperature (Tenv), whereby two switching temperatures (Tsw) have to be exceeded to enable the subsequent shape changes from shape (A) to shape (B) and finally the original shape (C). In this work, we explored the thermally and magnetically initiated shape-memory properties of triple-shape nanocomposites with various compositions and particle contents using different shape-memory creation procedures (SMCP). The nanocomposites were prepared by the incorporation of magnetite nanoparticles into a multiphase polymer network matrix with grafted polymer network architecture containing crystallizable poly(ethylene glycol) (PEG) side chains and poly(ε-caprolactone) (PCL) crosslinks named CLEGC. Excellent triple-shape properties were achieved for nanocomposites with high PEG weight fraction when two-step programming procedures were applied. In contrast, single-step programming resulted in dual-shape properties for all investigated materials as here the temporary shape (A) was predominantly fixed by PCL crystallites.