  Type IIA on the conifold is a prototype example for engineering QED with one
charged hypermultiplet. The geometry admits a flop of length one. In this
paper, we study the next generation of geometric engineering on singular
geometries, namely flops of length two such as Laufer's example, which we
affectionately think of as the $\it{conifold\ 2.0}$. Type IIA on the latter
geometry gives QED with higher-charge states. In type IIB, even a single
D3-probe gives rise to a nonabelian quiver gauge theory. We study this class of
geometries explicitly by leveraging their quiver description, showing how to
parametrize the exceptional curve, how to see the flop transition, and how to
find the noncompact divisors intersecting the curve. With a view towards
F-theory applications, we show how these divisors contribute to the enhancement
of the Mordell-Weil group of the local elliptic fibration defined by Laufer's
example.
