Since the rise of Cognitive Linguistics, prepositional polysemy has become a heated topic and invited treatments of a great number of cognitive linguists. Among them, Tyler and Evans (2003) have been holding sway with their “Principled Polysemy Model”, in which they develop a more constrained semantic network for over. The present study is a critique of this model. By revisiting some typical examples among the 14 postulated additional senses of over, it is revealed that it exhibits three flaws:(1) a misleading premise, which regards meanings that come about on the basis of the preposition over and other words as the basic meaning of over;(2) assuming still redundant and erroneous polysemy for over;(3) frequent mismatched examples. This study suggests a minimal polysemy approach and reveals the significance of tracing back to the nature of prepositional meanings in probing into prepositional polysemy.