shake a stick at
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more (something) than you can shake a stick at
A very large number; an amount that is more than one can count. When it comes to family members, Jay has more than you can shake a stick at.
shake a stick atSlang
To point out, designate, or name: "All of a sudden there came into being a vast conservative infrastructure: think-tanks ... and more foundations than you could shake a stick at" (National Review).