The Functional Mock-up Interface (FMI) is the standard for exchanging industrial simulation models in a variety of different applications. Although sensitivity analysis for continuously differentiable systems is directly supported by the standard, for systems with state discontinuities, it is only possible to determine correct sensitivities to a limited extent. In this position paper, we investigate how sensitivity analysis for discontinuous Functional Mock-up Units (FMUs), i.e. including state and time events, works in theory and which additional steps are required to obtain correct results in practice. We further investigate that these steps are unnecessarily computationally intensive from a mathematical point of view, but cannot be implemented in a more efficient way under the current restrictions of the standard. We therefore make a concrete proposal for the new layered standard sensitivity analysis (LS-SA) that remedies the current deficits of FMI in the sensitivity analysis of discontinuous systems. In this way, LS-SA opens FMI towards a variety of next-level applications — including (scientific) machine learning and optimal control — by providing fully differentiable FMUs under high computational performance.