Nowadays virtually every aeroplane has one pair of wings; they are monoplanes. Biplanes with two pairs of wings were very common in their day, and at least one triplane- the Fokker DR1 with three pairs of wings- became famous during the First World War as the machine flown by Baron von Richthoven. But things did not stop there; at the time writing the record appears to be 200 wings. Yes, two hundred. Obviously this is something that needs investigation.
There is a Wikipedia multiplane page dedicated to aero planes with more wings than a triplane.
AERODYNAMICS
Before and during the First World War two major discoveries in aerodynamics were made, that are highly relevant to examining early aeroplanes:
Aspect ratio. The aspect ratio of a wing is the ratio between its span (the distance between the wingtips) and the chord. (The distance from the leading edge to the trailing edge) A high aspect ratio, ie wings that have a span large with respect to the chord, are more efficient as the lift-to-drag ratio increases. Wikipedia gives a very good introduction. The importance of aspect ratio was recognised by the Wright brothers Their 1900 and 1901 gliders had low aspect ratio wingsof 3.4 and 3.3 respectively. From their wind tunnel data, the Wrights discovered that a high aspect ratio wing generated more lift and less drag than a low aspect ratio. The aspect ratio for their next glider in 1902 was 6.7, it it was very successful. The Wright Flyer had an aspect ratio of 6.4. Modern light aircraft have an aspect ratio of around 7.
Aerofoil thickness. Early aero planes had thin wing sections as this was believed (incorrectly) to give good lift/drag ratios. Thin airfoils showed “thin airfoil stall” at low angles of attack, due to the separation of the flow over the top surface of the thin airfoil, creating much higher drag and a loss of lift. Under the same conditions, thicker airfoils did not suffer flow separation until much higher angles of attack, hence producing more lift and less drag. This was discovered by German engineers, and thick airfoils were employed on the Fokker Triplane and the Fokker D-7 from late 1917 onwards. These machines could climb faster and maneuver more sharply than aeroplanes with thin airfoils; the Fokker D-7 was one of the most effective fighters of the First World War.
THE TRIPLANES: THREE PAIRS OF WINGS
We start with triplanes because most people are only aware of one- the Fokker DR1. In fact there were many, though it was never as popular a configuration as the biplane. There is a List of Triplanes in Wikipedia which gives 123 designs, though not all of these were flown, and only a few entered any sort of quantity production.
Triplanes have an excellent Wikipedia page of their own.

| Left: The British Sopwith triplane: 1917
The Sopwith Triplane did not have a particularly strong airframe, and you could literally pull the wings off it by pulling out of a relatively modest dive.
The Sopwith triplane has a Wikipedia page. There is more information here.
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| Left: The German Fokker DR-1 triplane: 1917
This is the most famous triplane, as flown by Baron von Richthoven; it is in fact the only one most people have heard of, but the truth is it was a reaction to the British Sopwith Triplane, which began operations in early 1917. The Fokker triplane served from the autumn of 1917 until the Armistice in November 1918. The DR-1 was slower than most of its contemporary rivals but it had efficient thick wings which gave it an exceptional rate of climb and a very tight turning circle, to allow it to compete with the Sopwith triplane. Some 300 or more were built but none of the original planes have survived; there are a number of replicas.
So far as is currently known the Sopwith triplane was withdrawn from service before the Fokker appeared, and there is no record of the two types fighting each other.
There is more info here.
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THE QUADRUPLANES: FOUR PAIRS OF WINGS
Quadruplanes do not have a Wikipedia page of their own, but a sub-section of the Wikipedia multiplanes article; see Quadruplanes.

| Left: The Wight quadruplane: 1919?
The Wight {not Wright) Quadruplane was designed in 1916. Remarkably, its wingspan was less than its overall length. It looks like a neat design but the wing design proved ineffic1ent and controllability was poor. In February 1918 it crashed into a cemetery and the project was abandoned.
The Wight Quadruplane has a Wikipedia page.
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| Left: The Zerbe Air Sedan: 1919?
The Zerbe Air Sedan was a single-engine quadruplane passenger aircraft designed by 'Professor' James Slough Zerbe in the USA in 1918. The machine made one flight in 1921, was damaged during landing, and was subsequently abandoned. There is a Wikipedia page.
"One of the first airliner concepts conceived by Jerome 'James' Slough Zerbe (1849-1921), different sources claim different years: 1909, 1910, 1914, 1918 or 1919. Reports claim the photo shows the quadruplane to be readied for test flight in 1919 at the Fayetteville, Arkansas fair grounds. Reports say the plane took off very quickly, rose to about 100 ft (30 m), flew approximately 1000 ft (300 m), and landed damaging its landing gear. After that Zerbe left town never to be heard of or seen again. What happened to the abandoned damaged plane is unknown."
To me the design of the cowling and propellor design suggest a later date, possibly 1919 but certainly not 1909. Wikipedia says the year of the flight was 1921.
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| Left: The Supermarine Nighthawk: 1917
The Supermarine Nighthawk PB 31E was intended to catch Zeppelins. It never did, because it was unable to reach Zeppelin height
It was designed by a young R J Mitchell, who went on to be the chief designer of the rather more successful Spitfire. The Nighthawk was a huge quadruplane, nearly 18 feet high with a wingspan of 60 feet. The four wings provided a large surface area while being relatively light for their structural strength, an idea designed to allow the Nighthawk to intercept German airships. However the plane was distinctly underpowered and took an hour to reach 10,000 feet. Bad enough, but since mid-level Zeppelins commonly flew several thousand feet above that, the plane was quite useless. Maximum speed was 75 mph in theory, but a pitiful 60 mph in reality.
There is more information here.
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| Left: The Supermarine Nighthawk: 1917
A steerable searchlight, with a separate power supply, (a petrol-electric generator?) was mounted in the plane’s nose; a 37 mm Davis gun on the top was its main armament. There were also two 0.303 Lewis guns. There were four crew members, two of which were gunners.
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THE QUINTAPLANES: FIVE PAIRS OF WINGS

| Left: The Zerbe Quintaplane: 1908?
Before building his Air Sedan (above, 4 wings) Zerbe had also designed not one but three quintaplanes with five staggered wings; see Wikipedia.
There is more information on this quintaplane here,
and also here.
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THE HEXAPLANES: SIX PAIRS OF WINGS

| Left: The Zerbe hexaaplane: 1908
Also previous to his four-winged Air Sedan (see above) Zerbe had designed a hexaplane with six staggered wings; see Wikipedia. It was again a large aeroplane with a single tractor engine. It is unknown if this machine was ever flown and if so what happened. The fact that there actually appears to be no engine installed here suggests it was never completed.
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This aeroplane has a Wikipedia page. Note you can call it a hexaplane or a sextuplane.
THE SEPTAPLANES: SEVEN PAIRS OF WINGS

| Left: The Marquis multiplane: 1907
This is a well-known photograph, but technical details are lacking. It was built in 1907 by the Marquis d'Ecquevilly, but never flew. It was destroyed in a fire in June 1908, and d'Ecquevilly built a new version design with fifty (yes, fifty) pairs of wings instead of six; this never flew either.
The wings are simple flat plates, which make a very poor aerofoil. There is also no visible means of control, not even a rudder; it could not have flown successfully. The oval hoops were 16 feet across and the engine was a 10 HP Buchet, geared down by a belt and pulleys. The machine was destroyed in a fire, and the Marquis went on to design a multiplane with 25 pairs of wings.
There is more information here. The Marquis multiplane is not mentioned in the Wikipedia multiplane article.
Photo location: Arles?
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| Left: The Gerhardt Cycleplane: 1908
The Gerhardt Cycleplane was developed in 1923 by Dr. William F Gerhardt, the head of the Aeronautical Engineering Department at the University of Michigan. It had seven wings of very high aspect ratio, presumably to minimise induced drag. The aerofoils appear to be of very thin section and therefore inefficient. The aircraft first flight was made on July 1923. In the first flight tests, an automobile towed the Cyleplane into the air and released it. The only human-powered takeoff of the Cycleplane was a short hop of 20 feet, rising only two feet.
The Cycleplane came to an inglorious end, collapsing into a pile of wreckage during a test run. The cine film of the accident is well-known and you can see it on YouTube.
There is a Wikipedia page.
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THE OCTAPLANES: EIGHT PAIRS OF WINGS
Typing 'octaplanes' into Google doesn't yield anything useful; mainly imaginary aircraft and eight-rotor drones.
THE MULTIPLANES: LOTS OF PAIRS OF WINGS

| Left: The Marquis multiplane: 1908
It was built in 1907 by the Marquis d'Ecquevilly, after his earlier septaplane was destroyed in a fire. There are allegedly 50 wings on this machine, but that actually means 25 pairs of wings. The wings are so close together that it seems highly unlikely they could have operated properly. In any case the wings appear to be simple flat plates (ie un-cambered) and so would not be effective. Note Monsieur Dupont looking on.
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