The variation of the molecular architecture of multiblock copolymers has enabled the introduction of functional behaviour and the control of key mechanical properties. In the current study, we explore the synergistic relationship of two structural components in a shape-memory material formed of a multiblock copolymer with crystallizable poly(ε-caprolactone) and crystallizable poly[oligo(3S-iso-butylmorpholine-2,5-dione)] segments (PCL-PIBMD). The thermal and structural properties of PCL-PIBMD films were compared with PCL-PU and PIBMD-PU, investigated by means of DSC, SAXS and WAXS measurements. The shape-memory properties were quantified by cyclic, thermomechanical tensile tests, where deformation strains up to 900% were applied for programming PCL-PIBMD films at 50 °C. Toluene vapor treatment experiments demonstrated that the temporary shape was fixed mainly by glassy PIBMD domains at strains lower than 600%, with the PCL contribution to fixation increasing to 42±2% at programming strains of 900%. This study into the shape-memory mechanism of PCL-PIBMD provides insight into the structure-function relation in multiblock copolymers with both crystallizable and glassy switching segments.