Advances in computational structure prediction will vastly augment the hundreds of thousands of currently-available protein complex structures. Translating these into discoveries requires aligning them, which is computationally prohibitive. Foldseek-Multimer computes complex alignments from compatible chain-to-chain alignments, identified by efficiently clustering their superposition vectors. Foldseek-Multimer is 3-4 orders of magnitudes faster than the gold standard, while producing comparable alignments; allowing it to compare billions of complex-pairs in 11 hours. Foldseek-Multimer is open-source software: github.com/steineggerlab/foldseek, webserver: search.foldseek.com and the BFMD database.

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