Network alignment aims to find conserved regions between different networks. Existing methods aim to maximize total similarity over all aligned nodes (i.e. node conservation). Then, they evaluate alignment quality by measuring the amount of conserved edges, but only after the alignment is constructed. Thus, we recently introduced MAGNA (Maximizing Accuracy in Global Network Alignment) to directly maximize edge conservation while producing alignments and showed its superiority over the existing methods. Here, we extend the original MAGNA with several important algorithmic advances into a new MAGNA++ framework.