Abstract The emerging concept of multi-caloric effects, introduced in 2010, entails the application of multiple interplay fields to a thermodynamic system. While multi-caloric effects are the main focus of experimental endeavors, theoretical considerations fall short of providing a thorough understanding. This paper introduces a comprehensive presentation on multi-caloric effects, employing the method and theory of exterior derivative formations. It addresses every aspect of thermodynamic systems, showcasing its applicability to multi-caloric materials (both single-phase and multi-phase materials), and its adaptability to different scenarios (either in single or multiple force fields). The formulation of Maxwell relationships, characterized by their generality and universality, enables a clear prediction in entropy and temperature, facilitating a distinct identification between independent and interdependent contributions from multi-caloric effects. These insights hold significant importance in designing and developing specialized thermodynamic materials, optimizing functional performances and exploring innovative mechanisms.