A fundamental challenge in physics is controlling the propagation of waves in disordered media despite strong scattering from inhomogeneities. Spatial light modulators enable one to synthesize (shape) the incident wavefront, optimizing the multipath interference to achieve a specific behavior such as focusing light to a target region. However, the extent of achievable control was not known when the target region is much larger than the wavelength and contains many speckles. Here we show that for targets containing more than g speckles, where g is the dimensionless conductance, the extent of transmission control is substantially enhanced by the long-range mesoscopic correlations among the speckles. Using a filtered random matrix ensemble appropriate for coherent diffusion in open geometries, we predict the full distributions of transmission eigenvalues as well as universal scaling laws for statistical properties, in excellent agreement with our experiment. This work provides a general framework for describing wavefront-shaping experiments in disordered systems.