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We analyze the charge-to-mass structure of BPS states in generalinfinite-distance limits of $\mathcal{N}=2$ compactifications of Type IIBstring theory on Calabi-Yau three-folds, and use the results to sharpen theformulation of the Swampland Conjectures in the presence of multiple gauge andscalar fields. We show that the BPS bound coincides with the black holeextremality bound in these infinite distance limits, and that thecharge-to-mass vectors of the BPS states lie on degenerate ellipsoids with onlytwo non-degenerate directions, regardless of the number of moduli or gaugefields. We provide the numerical value of the principal radii of the ellipsoidin terms of the classification of the singularity that is being approached. Weuse these findings to inform the Swampland Distance Conjecture, which statesthat a tower of states becomes exponentially light along geodesic trajectoriestowards infinite field distance. We place general bounds on the mass decay rate$\lambda$ of this tower in terms of the black hole extremality bound, which inour setup implies $\lambda \geq 1/\sqrt{6}$. We expect this framework topersist beyond $\mathcal{N}=2$ as long as a gauge coupling becomes small in theinfinite field distance limit.

Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes