Generally, conventional moment-resisting frames are prone to substantial residual displacements. To overcome this disadvantage, self-centering systems were introduced. Post-tensioned self-centering (PTSC) moment-resisting systems are a variation of conventional moment-resisting systems that drastically reduce the large residual displacements of the moment frames. However, one of the uncommon drawbacks identified in PTSC systems is their low energy dissipation. This study aims to compensate for this by innovatively combining conventional self-centering systems with special moment-resisting frames (SMRF) in various formats to retain the advantages of both systems. Another disadvantage of PTSC systems is the high cost and complexity of the structural design procedure required to maintain an elastic response in the framing beam-column elements. To address this issue, a practical and cost-effective design procedure was proposed. The study also included the influence of different dual SMRF-PTSC frame actions and base column connection types. A set of 35 structures comprising 4, 8, 12, and 16-story buildings were considered for nonlinear static/dynamic analysis and seismic response assessment. The nonlinear static analyses were carried out in a cyclic format due to the self-centering characteristics of the system. Additionally, 22 far-field records per FEMA P695 were chosen for the time history analyses. The results show that structures equipped with post-tensioned self-centering connections (PTSC) designed according to the proposed procedure are successful in drastically decreasing residual drifts. However, the total elimination of residual drifts relies on providing a self-centering connection for the base level columns and considering an overstrength factor for the base level columns' moment capacity design. The proposed value in this investigation was derived as 5, which significantly strengthens the base level columns while resulting in an overall notably cost-efficient PTSC-equipped frame. In the case of dual frames, the conventional SMRF spans should not exceed the number of PTSC-equipped spans, as doing so will diminish the self-centering characteristics of the lateral system.