The paper introduces Codomain Attention Neural Operator (CoDA-NO), a novel neural operator architecture designed to solve multiphysics partial differential equations (PDEs) with complex geometries and interactions between physical variables. CoDA-NO tokenizes functions along the codomain or channel space, enabling self-supervised learning and pretraining of multiple PDE systems. The architecture extends positional encoding, self-attention, and normalization layers to function space, allowing it to learn representations of different PDE systems with a single model. Evaluations on fluid flow simulations and fluid-structure interaction tasks show that CoDA-NO outperforms existing methods by over 36% in few-shot learning settings, demonstrating its effectiveness in handling complex downstream tasks with limited data. The code for CoDA-NO is available at <https://github.com/ashiq24/CoDA-NO>.The paper introduces Codomain Attention Neural Operator (CoDA-NO), a novel neural operator architecture designed to solve multiphysics partial differential equations (PDEs) with complex geometries and interactions between physical variables. CoDA-NO tokenizes functions along the codomain or channel space, enabling self-supervised learning and pretraining of multiple PDE systems. The architecture extends positional encoding, self-attention, and normalization layers to function space, allowing it to learn representations of different PDE systems with a single model. Evaluations on fluid flow simulations and fluid-structure interaction tasks show that CoDA-NO outperforms existing methods by over 36% in few-shot learning settings, demonstrating its effectiveness in handling complex downstream tasks with limited data. The code for CoDA-NO is available at <https://github.com/ashiq24/CoDA-NO>.