Last night, Mr. Met took his cap off during the game.
I always thought the cap was part of the main head of the costue, but I guess now that I think about it, sometimes Mr. Met does wear a black cap so they are clearly swappable.
But it appears to come off somewhat easily, so now I am surprised that rubes don’t constantly try to knock it off his head and/or steal it. Fortunately, Mets fans are well behaved.