The Republic, The New Kingdom, The Old Kingdom, The Scyther Republic, and... I don't remember the fifth. And technically the New Kingdom and the Republic aren't fighting each other ( even being passively aligned) and the Old Kingdom is mostly alright with the New Kingdom as long as the New Kingdom doesn't challenge the Old Kingdom's weak claim to the throne, surrenders the Old Crown, which has passed to Tune, and doesn't try to take any new territory. And of course, the Scyther Republic has conquered The Republic. So now you've got the enmity of The Republic's army ( as much as it remains ) and The Old Kingdom. A brief description of the factions I remember:
The Republic - The Republic of Cheesistan, under President Rhett/Yusef whose capitol is Microphonia.
The New Kingdom - The throne/crown of Cheesistan as claimed by Tune on technicality since it was never legally abolished.
The Old Kingdom - A group of old agents of the king and/or transitional government and very low ranking nobles with weak claim to the throne, guided by a charismatic former adviser to the king named Klaus. They act in secret and were fine running the provisional government of the few people left in Cheesistan and/or doing business abroad, but the recent events have caught their eye and drawn them back. They are based at the old Lakeside vacation palace of the royal family, which Klaus has legal ownership of, being granted it by the old king. They haven't really been important in the story yet.
Scyther Republic - The People's Scyther Republic of Cheesistan and Outlying Soviets - SRC - The nebulous Communist government established by Comrade Poketwo. It's power is shaky, but officially they have control of Microphonia. The President has fled to safety and noone outside of Microphonia acknowledges their sovereignty. The Microphonia citizens only do, because well... You just fucked over the Cheesistani military and forcibly took their government center and fear is a powerful motivator.
Also expect Rebel forces that want to either establish their own government or restore the Republic or the Old Kingdom.