关于短语动词,He take off his hat,这句话中take off是短语动词,He take his hat

关于短语动词,
He take off his hat,这句话中take off是短语动词,He take his hat off 中take off也是短语动词,只是它的宾语his hat放在中间了,可是在另一句话中,He take his hat off his head,是不是在这里off his head是介词短语,而off不跟take合成短语动词了?就像I put my hat on the table 中,on the table 在一起一样?
您说得我看明白了，但是还有疑问，您的意思是不管什么时候off都是和前面的take组成短语动词？那么难道最后一句I put my hat on the table中的on也跟前面？那么怎么解释问句Where do you take your hat的问句？这个问句是以off his head提问的