Same-dip double-subduction (SDDS) systems are widely reported from present as well as past complex convergent plate tectonic configurations. However, the dynamics of their evolution is poorly understood, which is crucial to conceptualize anomalous subducting slab kinematics and associated observed geological phenomena, such as irregular trench migration rates, high convergence velocities, and slab break-off. To bridge this gap, we develop dynamic thermo-mechanical subduction models and investigate the initiation and evolution of SDDS systems, considering three different initial plate configurations: oceanic, oceanic-continental and multiple continental settings, based on Neo-Tethyan paleo-reconstructions. Each model offers new insights into the complex tectonic history of the major Neo-Tethyan subduction zones, particularly the Indo–Eurasian and Andaman convergent systems. We evaluate the slab-slab interactions, trench and subduction kinematics, inter-plate reorganization, and temporally varying mantle flow patterns involved in the dynamic evolution of these SDDS systems. The oceanic SDDS model simulations reveal that a sizable oceanic plate can initiate two subduction zones synchronously, and they evolve unequally in a competing mode, leading to exceptionally high convergence rates (∼16–17 cm/year) for a prolonged duration (∼7–8 Myr). This finding explains the coeval activity of coupled subduction zones in the Indo-Eurasia convergence during the Cretaceous evolution of the Neo-Tethys. We further implement a corresponding single subduction model to assess the additional effects of competing slab kinematics in an oceanic SDDS setting. The ocean-continent SDDS model, on the other hand, localizes subduction preferentially at passive margins between the oceanic plate and the continental block, forming double subduction zones that grow almost equally to form a spreading centre between the two trenches. These model results allow to reconstruct the Cenozoic evolution of the eastern Neo-Tethyan region, which ultimately led to the development of the Andaman subduction zone. We also show the post-Cretaceous evolution of the Indo–Eurasian collision zone as a consequence of the SDDS dynamics in presence of multiple continental blocks. These dynamics facilitated slab break-off, transforming the SDDS into a single subduction system in a relatively short time frame (∼3 Myr). We finish with a synthesis of the paleo-reconstructions of the Neo-Tethys in the perspective of these SDDS models.