Summary: In a recent paper DeWolfe et al. have shown how to use the self-intersection number of junctions to constrain the BPS spectrum of \(N=2\), \(D=4\) theories with ADE flavor symmetry arising on a single D3-brane probe in a 7-brane background. Motivated by the existence of more general \(N=2\), \(D=4\) theories arising on the worldvolume of multiple D3-brane probes we show how to compute the self-intersection number of junctions in the presence of 7-branes and multiple D3-branes.