By 1915, Quadrangle determined that the McCosh was not large enough (or grand enough). The following year, it sold the McCosh House to Lloyd Grover, who moved it to its current location on Nassau Street, a block from the intersection with Harrison Street. Quad then commissioned one its board members, Henry Milliken, Class of 1905, to design a new building.

Milliken's plan for Quad called for a classic brick Georgian Revival structure, with the corners defined by white quoins and featuring a large entrance portico. In choosing a Georgian model, Milliken inevitably invited comparisons to Charles McKim's Cottage Club two doors down the street, but for reasons of economy he was constrained in his ambitions.