more someone or something than one can shake a stick at
Rur. a lot; too many to count. There were more snakes than you could shake a stick at.There are lots of flowers in the field—more than one can shake a stick at.
A large quantity, more than one can count, as in Our town has more banks than you can shake a stick at. This idiom presumably refers to brandishing a stick as a weapon, but the precise allusion is unclear. [Colloquial; c. 1800]