We conduct a model-independent analysis of processes involving $|\Delta b|=|\Delta d|=1$ transitions, aiming to test the standard model and explore flavor patterns of new physics. Exploiting the current data from $B^+ \to \pi^+ \,\mu^+\mu^-$, $B^0_s\to \bar{K}^{*0}\, \mu^+\mu^-$, $B^0\to\mu^+\mu^-$, and radiative $B \to X_d \,\gamma$ decays, we derive constraints on Wilson coefficients through global fits. The fit results are consistent with the standard model but show significant potential for new physics contributions at experimental facilities like LHCb and Belle II, or a future $e^+ e^-$ collider.