The late-time modifications of the standard Λ Cold Dark Matter (ΛCDM) cosmological model can be parameterized by three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the Large Scale Structure. In this Letter, we present the first joint reconstruction of these three functions performed in a non-parametric way from a combination of recent cosmological observations. The reconstruction is performed with a theory-informed prior, built on the general Horndeski class of scalar-tensor theories. We find that current data can constrain 15 combined modes of these three functions with respect to the prior. Our methodology enables us to identify the phenomenological features that alternative theories would need to have in order to ease some of the tensions between datasets within ΛCDM, and deduce important constraints on broad classes of modified gravity models.