We explore the phenomenological consequences of general late-time modifications of gravity in the quasi-static approximation, in the case where baryons and cold dark matter have distinct couplings to the gravitational sector. Assuming spectroscopic and photometric surveys with configuration parameters similar to those of the Euclid mission, we derive constraints on our effective description from three observables: the galaxy power spectrum in redshift space, tomographic weak-lensing shear power spectrum and the correlation spectrum between the integrated Sachs-Wolfe effect and the galaxy distribution. In particular, with $\Lambda$CDM as fiducial model and a specific choice for the time dependence of our effective functions, we perform a Fisher matrix analysis and find that the unmarginalized $68\%$ CL errors on the three parameters describing the modifications of gravity are of order $\sigma\sim10^{-3}$. We also consider two other fiducial models. A nonminimal coupling of CDM enhances the effects of modified gravity and reduces the above statistical errors accordingly. In all cases, we find that the parameters are highly degenerate, which prevents the inversion of the Fisher matrices. Although all three observational probes are complementary in breaking some of the degeneracies, the ISW-galaxy correlation stands out as a promising probe to constrain the modifications of gravity.