In this paper we will describe the synthesis and properties of two series of high molecular weight segmented block copolymers from all-aromatic amorphous (AM) or liquid crystal (LC) telechelic ester-based maleimide-functionalized oligomers (M_n = 5 kg mol^-1) and telechelic thiol-terminated poly(dimethylsiloxane) (PDMS, M_n = 1, 5 and 10 kg mol^-1). The multiblock copolymers were prepared via highly efficient thiol-ene click chemistry, and have M_ns ranging from 22 to 58 kg mol^-1. The segmented block copolymers prepared from mesogenic (LC) units show micro-phase separation and liquid crystallinity even with a PDMS content as high as 65 wt%. The AM5K-based series is completely amorphous. The multiblock copolymers with PDMS5K and 10K show two T_gs at ∼-120 °C and ∼120 °C, respectively, implying the presence of a (micro)phase separated system. The multiblock copolymer prepared from AM5K and PDMS1K displays excellent stress-strain behavior at 25 °C, with a tensile strength of 123.6 MPa, an elastic modulus of 3.4 GPa, an elongation at break of 31.2% and toughness of 30.7 MJ m^-3. The LC5K based multiblock copolymer films exhibit poor stress-strain behavior, which is the result of a higher degree of phase separation and low phase intermixing, as confirmed by TEM measurements. The shape memory properties of the PDMS-containing segmented block copolymers in the temperature range of -150 to 150 °C were tested using a rheometer in torsion mode. The glass transitions originating from the rigid aromatic blocks and flexible PDMS blocks were used as the reversible switches for designing T_g-based dual- and triple-shape memory polymer films. The AM5K-b-PDMS1K and LC5K-b-PDMS1K multiblock copolymers show dual-shape memory behavior in the temperature range of 20-150 °C. The PDMS5K based analogs show triple shape-memory behavior in the temperature range of -150-150 °C.