Would you agree that the expressions below share only ONE (metaphorical) meaning in common:
turn something on its head
turn something upside down
turn something on its head - (also: stand something on its head) cause a complete reversal of what is regarded as the norm: Suddenly, Jayne's once sane life is turned on its head, and not even her closest friends are what they seem.
turn something upside down - 1. reverse smth. physically: Wolfe uncorked the bottle and turned it upside down. The water splashed the stones at Mr. Turrell's feet.
2. = turn something on its head: That would have turned charity tax law upside down.
3. search everywhere in a place, especially roughly: The police turned his flat upside down looking for drugs.