"Throw one's cap over the windmill" is an idiomatic expression used to describe someone who is overly optimistic or unrealistic about their goals. However, there are several other synonyms that one can use in place of this particular phrase. One of the most common alternatives is "tilting at windmills," which refers to battling imaginary enemies. Another synonym is "chasing wild geese," which means pursuing something that's impossible to catch or achieve. Other idiomatic expressions that can be used in place of "throw one's cap over the windmill" include "building castles in the air," "pursuing a wild goose chase" and "daydreaming." All these synonyms portray a sense of unrealisticness.