1918 was already stretching it. Russia already had a revolution that knocked it out of the war, and some units in the French army were just about ready to kill each other.
To extend the war, an interesting notion would be to have one side or both marred by alternate forms of extremism in the years leading to the war. Britain and the Soviet Union took far more damage on the home front in World War II than they did in World War I, yet still held on to the end, as the Germany they would be surrendering to was demonstrably more extremist, intolerant of their own systems and set on the actual occupation and destruction of their countries, whereas Imperial Germany would at most demand colonies, economic concession and relatively little shifts in the borders of Europe. Making World War I the 'War of Annihilation' the propaganda made it out to be would do a good bit towards keeping the people 'on-side' for longer.
To do that, PoD before 1900 may be required. A 'Red Spring' could suffice, revolutions succeeding in some countries and failing in others. Communist Britain and France in the later 1800's seems like the most possible, with PoDs involving harsher reaction to union demands for worker's rights and the Franco-Prussian War's aftermath serving as the window for a revolution to begin. They'd both have trouble making the colonies follow suit, Canada almost certainly a lost cause, but Britain's navy keeps Australia and Asia close enough to keep hold of, French Africa is still close enough for an even more unstable France, and both would likely have each other for support, instead of having the Entente Cordiale signed only in 1904. Russia is tougher, they really needed to have a big war for the communists to get a window, and their position on the other side of Germany is crucial to not make the war a stomp for the German-centred anti-communists. A solution would be for the German army to decide upon a 'Russia First' strategy, or for the war to start off as a Russo-German war, and the Entente offering Russia a deal with 'The enemy of my enemy is my friend'.
This could mould the main three deciding participants of the war into more extreme systems willing to take so much punishment for years on end (Britain and France as bold global pariahs trying to encourage a new world order, and Germany a powerful young force with a revolution to crush) and keep the fourth (the United States) out of the whole business. It would also help out Austria-Hungary, as Italy would more likely side with the Central Powers.
A more successful suffragette movement could,
could, lead to a longer possible war. Putting women into the factories, or even on the front, means a greater utilisation of labour and longer before one side or the other breaks. The USSR made use of women as tank crews and pilots. It could easily fall into dieselpunk trappings

, although many of those stories are indeed inspired by imagining a longer Great War.