Thermoplastic and thermoset all-aromatic liquid crystal (LC) (AB)n-multiblock copoly(ester imide)s based on N-(3′-hydroxyphenyl)trimellitimide (IM), 4-hydroxybenzoic acid (HBA), and 6-hydroxy-2-naphthoic acid (HNA) were investigated as single-component high-temperature (≥250 °C) shape memory polymers (SMPs). A high Tg (∼200 °C) HBA/IM block embedded in a low Tg (∼120 °C) HBA/HNA matrix creates a stable rubbery plateau that can be extended to ∼240 °C by cross-linking. The shape fixation (Rf) and shape recovery efficiency (Rr) of the thermoplastic and thermoset films were investigated using a rheometer in torsion mode. Thermoplastic LC copoly(ester imide) films showed excellent dual SM behavior (Rf and Rr ∼ 100%) at 170 °C. After cross-linking the thermoplastic films a single component system as obtained that exhibited high-temperature (≥250 °C) tunable triple SM and one-way reversible SM behavior.