A Theoretical System is the conceptual structure that a scientific community uses in developing testable theories and interpreting data it is also referred to as a paradigm.
A scientific community’s theoretical system is considered to be true by that community and its core concepts are generally fixed and not subject to change with new data. 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.
The key to understanding theoretical systems is that they can only be evaluated internally because they are self contained systems. Different theoretical systems often 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.