Eleven Years' War in Ireland comes to mind (although there were occasional alliances), then there are French Wars of Religion (notably the War of the Three Henrys), more recently the Bosnian War and Angolan Civil War (with various factions fighting each other). I'm pretty sure there are some examples in the Japanese history (though I can't name any).

As for battles, Battle of Bosworth Field fought during the Wars of the Roses might qualify, although Sir Stanley held back while he decided which side it would be more advantageous to support.

I'm sorry, but I've had to remove this as it runs afoul of the rules we have in place about "Throughout History".

But, I don't want you to leave empty handed, so I would recommend you look into the Mexican Revolution, specifically the American Punitive Expedition to hunt down Pancho Villa. Villa was in rebellion against the Mexican government, and his men raided Columbus, New Mexico, leading to a lot of anger in the US. An expedition was mounted to hunt him down in Mexico, but the Mexican government wasn't pleased with this. Which meant that there were three distinct sides, all of whom clashed with the other two at some point during those months. (And while I'm a bit occupied, I'd love to write up something longer for you later today, so if you want to ask a specific question on that matter, please do!)