"And he wears a hat on a hat" ... What is it like?
The most successful of them are not literally perceived (what he put on over one headgear of the other), but the type of wearing a hat. That is, “a hat wears ON a hat” will be synonymous with the phrase “a hat wears like a hat”. Another version suggests that "on the hat" is a hat with a certain curved crown. Another option: Bucket hat - the national headdress in some South American countries, their bucket hat in some way resembles a hat.