more than one can shake a stick at

• more than one can poke a stick at
• more than you can shake a stick at

Unknown. American English, in use since about 1800.^[1]

more than one can shake a stick at (comparative form only)

1. Occurring in abundance; of a large quantity; many.
   • 1851 June – 1852 April, Harriet Beecher Stowe, chapter 16, in Uncle Tom’s Cabin; or, Life among the Lowly, volume (please specify |volume=I or II), Boston, Mass.: John P[unchard] Jewett & Company; Cleveland, Oh.: Jewett, Proctor & Worthington, published 20 March 1852, →OCLC:

     "[L]aziness, cousin, laziness,—which ruins more souls than you can shake a stick at."

   • 1883, Edward Payson Roe, chapter 39, in His Sombre Rivals: A Story of the Civil War:

     "[H]e's laid out more 'Federates dan he can shake a stick at."

   • 1910, Jack London, chapter 16, in Burning Daylight:

     "I've got more companies than you can shake a stick at. There's the Alameda & Contra Costa Land Syndicate, the Consolidated Street Railways, the Yerba Buena Ferry Company, the United Water Company, the Piedmont Realty Company, the Fairview and Portola Hotel Company, and half a dozen more that I've got to refer to a notebook to remember."

   • 2004 August 15, Ben Stein, “For Sale: The Ultimate Status Symbol”, in New York Times, retrieved 12 June 2014:

     There are more billionaires than you can shake a stick at.

• The modified noun is placed between more and than.