  An irreducible 3--manifold with torus boundary either is a Seifert fibered
space or admits at most three lens space fillings according to the Cyclic
Surgery Theorem. We examine the sharpness of this theorem by classifying the
non-hyperbolic manifolds with more than one lens space filling, classifying the
hyperbolic manifolds obtained by filling of the Minimally Twisted 5 Chain
complement that have three lens space fillings, showing that the doubly
primitive knots in $S^3$ and $S^1 \times S^2$ have no unexpected extra lens
space surgery, and showing that the Figure Eight Knot Sister Manifold is the
only non-Seifert fibered manifold with a properly embedded essential
once-punctured torus and three lens space fillings.
