Physics Informed Neural Networks (PINNs) have been rarely applied to solve multiphysics systems due to the inherent challenges in optimizing their complex loss functions, which typically incorporate multiple physics-based terms. This study presents a multistage PINN approach designed to efficiently solve coupled multiphysics systems with strong interdependencies. The multistage PINN progressively increases the complexity of the physical system being modeled, enabling more effective capture of coupling between different physics. The computational merits of this approach are demonstrated through two illustrative applications: prediction of asphalt aging and modeling of lid-driven cavity flow. Quantitative and qualitative comparisons with standard PINN and adaptive weight PINN approaches demonstrate the enhanced precision and computational efficiency of the proposed algorithm. The multistage PINN achieves a reduction in training time of more than 90% compared to standard PINNs while maintaining better alignment with the finite element method (FEM) solutions. The improvement in computational efficiency, coupled with enhanced accuracy, positions the multistage PINN as a powerful tool for addressing complex multiphysics problems across various engineering disciplines. The method’s ability to handle interactions between multiple physical processes, such as diffusion, chemical reactions, and fluid dynamics, makes it suitable for simulating long-term material behavior and complex fluid systems.