Analogous to genomic sequence alignment, biological network alignment (NA) aims to find regions of similarities between molecular networks (rather than sequences) of different species. NA can be either local (LNA) or global (GNA). LNA aims to identify highly conserved common subnetworks, which are typically small, while GNA aims to identify large common subnetworks, which are typically suboptimally conserved. We recently showed that LNA and GNA yield complementary results: LNA has high functional but low topological alignment quality, while GNA has high topological but low functional alignment quality. Thus, we propose IGLOO, a new approach that integrates GNA and LNA in hope to reconcile the two. We evaluate IGLOO against state-of-the-art LNA (NetworkBLAST, NetAligner, AlignNemo, and AlignMCL) and GNA (GHOST, NETAL, GEDEVO, MAGNA++, WAVE, and L-GRAAL) methods. We show that IGLOO allows for a trade-off between topological and functional alignment quality better than the existing LNA and GNA methods considered in our study.