Of the true multiplanes with more than say four wings, the most famous is surely the Caproni "Capronissimo" nine-winged flying boat, having three triplane stacks in tandem. It crashed on its maiden flight, I cannot recall offhand whether through instability or structural failure.
Aerodynamically the most significant were the "venetian blind" types developed by the British scientist Horatio Phillips around 1900. In the late 19th century he had made major contributions to the study and theory of lifting aerofoils. He then developed an aerodynamic theory suggesting that multiple very narrow wings would be more efficient than a single large one. The first manned Phillips multiplane achieved a hop of around 50 ft in 1904. The next a few years later did a little better but fell way below his expectations or comparable conventional types, and in so doing it disproved his theory and he moved on to other studies.
Another was the AEA Cygnet designed by Alexander Graham Bell. Its wing comprised a fine grid of pyramidal cells and, when the Mk III finally got off the ground in 1912, it performed no better than Phillips' efforts. He paid back the Fates in spades by going on to develop that curse of modern society, the telephone.
Offhand I cannot recall any others.
One unflown design, which I here publish information on for the first time, was included in a provisional patent lodged by J.W. Dunne (of the tailless swept wing) in 1904. He had been working on wing rotors - flat horizontal-axis Magnus rotors which when stopped form wing surfaces - and had built models of them demonstrating automatic stability. These were the subject of his patent. One of the variants described was a multiplane assembly which formed a single rotor. What a sight that would have been! He was well informed and would have been aware of Phillips' work, so this would have been his stake in the ground had both their ideas come off. A copy of the provisional patent is in the Science Museum's Dunne collection and I have a photocopy of it. But there were no drawings to thumbnail and copyrights forbid any sensible posting of the text here, sorry about that.