We're all familiar with lots of non-functioning "democracies" that have internal strife all over the world. My question is whether a country that has has real, free elections and multiple parties has been displaced by something else (communism? authoritarianism?) in the modern era, and further whether it ever more successful than the democracy that came before it.
"Functioning" is obviously in the eye of the beholder (is a democracy that becomes authoritarian truly "functioning"?), but Weimar Germany seems to satisfy your requirement. It had real, free elections, with multiple parties. And yet... National Socialism. (Was National Socialism more successful than the Weimar Republic? I mean, depends on your metrics for success, obviously. I would say "no.")
There are plenty of other examples of democracies falling to "something else." Iran is another classic case, where a coup overturned a democratic parliamentary system and replaced it with something essentially authoritarian (the Shah).
Just to name two well-known examples from the 20th century.