Thermoplastics, while advantageous for their processability and recyclability, often compromise thermochemical stability and mechanical strength compared to thermosets. Addressing this limitation, we introduce an innovative approach employing reversibly cross-linked polymers, utilizing squaramide moieties to reconcile recyclability and robustness. Herein, we detail the synthesis of supramolecularly cross-linked polysquaramides through the condensation polymerization of diethyl squarate with primary and secondary diamines. This methodology embeds hydrogen-bonding squaramide motifs into the polymer chains, yielding materials with significantly enhanced storage moduli, reaching up to 1.2 GPa. Material characterization via dynamic mechanical analysis, creep-recovery, and stress relaxation experiments delineate a distinctive rubbery plateau across a broad temperature range, excellent creep resistance, and multimodal viscoelastic flow, respectively, attributable to the dynamic nature of the supramolecular cross-links. Additionally, the study showcases the modulation of glass transition temperature (Tg) by altering the monomer composition and stoichiometry, demonstrating the tunability of polymer viscoelastic properties through precise control over hydrogen bonding interactions. Overall, the incorporation of squaramide motifs not only provides the structural integrity and mechanical performance of these thermoplastics but also leads to engineering materials with tailored viscoelastic characteristics.