Some examples of interaction between dominant and non-dominant models in history of thought

What are the types of interaction between dominant and non-dominant models in history of ideas? Is it the case that dominant paradigms of thought and "absolute pre-suppositions" of one age are permeated with non-dominant, different or even opposite sets of ideas, pre-suppositions and beliefs? If so, to what extent? Is it possible to control trajectories of ideas, their circulation and historical interactions in processes of suppressing the non-dominant models (by eradicating material traces and destroying their proponents)? How do suppressed ideas influence dominant models of thought?