We propose that the superconducting diode (SD) efficiency can be significantly enhanced near the transition between two superconducting states by choosing parameters where, before the system goes normal with increasing supercurrent, it switches into a different superconducting order for one direction of the current but not for the other. This mechanism for producing high SD efficiency relies on the expectation that the critical current depends sensitively on the superconducting order. We demonstrate this explicitly by performing detailed calculations for a bilayer superconductor with an in-plane magnetic field, which admits the standard Bardeen-Cooper-Schrieffer (BCS) and the orbital Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) orders as a function of the strength of the magnetic field. We predict a sharp peak in the SD efficiency in the FFLO state close to the transition, which arises from a complex interplay between the two superconducting orders. An implication of our study is that the measurement of the SD efficiency can provide fundamental insight into the nature of the BCS-FFLO transition both as a function of the magnetic field and the supercurrent.