A Theoretical System is the conceptual structure used by a scientific community that forms the bases for developing testable theories and interpreting data it is also referred to as a paradigm.
A theoretical system of a scientific community is accepted as true by that community and it is generally fixed and not subject to change with new data. This is true only of core concepts to which theoretical patches are often added to make a theoretical system fit reality when reality is not what was originally expected. The theoretical system forms the bases for developing testable theories and interpreting data.
Examples of this come from origins sciences where there are two main theoretical systems. Biblical creation has a 6 days creation, a global flood and a young Earth. General evolution has the Big Bang cosmology, Nebula theory of star and planet formation, Uniformitarian Geology, Abiogenesis and Biological evolution. All other theoretical systems are basically mixtures of these two including old earth creation and theistic evolution.
A key to understanding theoretical systems is that they can only be evaluated internally because they are self contained systems. Different theoretical systems can produce different and even contradictory interpretations for the same evidence so that an interpretation from one theoretical system can not be used to disprove another because an interpretation from one theoretical system may not be valid in another.
Parts of a theoretical system can start out as testable theories and become so entrenched that they loose all testability by being patched to the point where they can absorb any new data. The Big Bang is a good example of this. It has be come so entrenched that there is no mainstream thought of abandoning it because contradicting data is absorbed when possible such as the accelerating expansion of the universe; which was by the invention of dark energy; or ignored such as the relationships between active galaxies and quasars.
Theoretical systems can have concepts in common but while different system may share some concepts while concepts are totally different. They are an unavoidable but little understood part of Science because data is not self interpreting and needs a theory on which to base the interpretation. Unfortunately it is often unclear as to where a testable theory end and theoretical system begins.