In this talk I will introduce the idea of Floer homotopy theory and show how it can be used to give lower bounds on degenerate Lagrangian intersections, in the case of plumbings of cotangent bundles along a submanifold. The strength of the invariant comes from incorporating all additional choices involved in the construction of the stable homotopy type, resulting in a parameterized spectrum. The work is joint with Kenneth Blakey.