We perform a global analysis of Beauty, Top, Z and Drell-Yan measurements in the framework of the Standard Model effective theory (SMEFT). We work within the minimal flavor violation (MFV) hypothesis, which relates different sectors and generations beyond the SU(2)L-link between left-handed top and beauty quarks. We find that the constraints on the SMEFT Wilson coefficients from the combined analysis are stronger than the constraints from a fit to the individual sectors, highlighting synergies in the global approach. We also show that constraints within MFV are strengthened compared to single-generation fits. The strongest bounds are obtained for the semileptonic four-fermion triplet operator C(3)lq, probing scales as high as 18 TeV, followed by the gluon dipole operator CuG with 7 TeV, and other four-fermion and penguin operators in the multi-TeV range. Operators with left-handed quark bilinears receive order one contributions from higher orders in the MFV expansion induced by the top Yukawa coupling as a result of the FCNC b→sμμ anomalies combined with the other sectors. We predict the 68% credible intervals of the dineutrino branching ratios within MFV as 5.3⋅10−6≤(B0→K∗0νν¯)≤12.8⋅10−6 and 2.5⋅10−6≤(B+→K+νν¯)≤5.9⋅10−6, which include the respective Standard Model predictions, and are in reach of the Belle II experiment. We show how future measurements of the dineutrino branching ratios can provide insights into the structure of new physics in the global fit.