Polymeric materials possessing specific features like programmability, high deformability, and easy processability are highly desirable for creating modern actuating systems. In this study, thermoplastic shape-memory polymer actuators obtained by combining crystallizable poly(epsilon-caprolactone) (PCL) and poly(3S-isobutylmorpholin-2,5-dione) (PIBMD) segments in multiblock copolymers are described. We designed these materials according to our hypothesis that the confinement of glassy PIBMD domains present at the upper actuation temperature contribute to the stability of the actuator skeleton, especially at large programming strains. The copolymers have a phase-segregated morphology, indicated by the well-separated melting and glass transition temperatures for PIBMD and PCL, but possess a partially overlapping T-m of PCL and T-g of PIBMD in the temperature interval from 40 to 60 degrees C. Crystalline PIBMD hard domains act as strong physical netpoints in the PIBMD-PCL bulk material enabling high deformability (up to 2000%) and good elastic recoverability (up to 80% at 50 degrees C above T-m,T-PCL). In the programmed thermoplastic actuators a high content of crystallizable PCL actuation domains ensures pronounced thermoreversible shape changes upon repetitive cooling and heating. The programmed actuator skeleton, composed of PCL crystals present at the upper actuation temperature T-high and the remaining glassy PIBMD domains, enabled oriented crystallization upon cooling. The actuation performance of PIBMD-PCL could be tailored by balancing the interplay between actuation and skeleton, but also by varying the quantity of crystalline PIBMD hard domains via the copolymer composition, the applied programming strain, and the choice of T-high. The actuator with 17 mol% PIBMD showed the highest reversible elongation of 11.4% when programmed to a strain of 900% at 50 degrees C. It is anticipated that the presented thermoplastic actuator materials can be applied as modern compression textiles.