While we know of countries balkanizing, is there any such thing as lower-level balkanizing? Like, some regions within a province balkanizing, becoming their own province while still staying a part of the same country, a neighborhood within a city leaving the city and becoming its own city, while still remaining part of the country, etc.
West Virginia splitting out because it opposed slavery is a good one. Also, the Soviets redrew or split out autonomous republics quite often.