The Kingdom of Burgundy (not to be confused with the later, aspired-to royal demesne of Charles the Bold), more frequently known as the Kingdom of Arles due to its capital, was a medieval state spanning what is now roughly the border region between France, Italy, and Switzerland. From around the 870's till the 1030's, it was an independent kingdom that frequently involved itself in dynastic struggles in northern Italy, while fending off attacks from both West and East Francia. It was occasionally split up into two northern and southern halves under different rules, and remained a free polity up until the heirless death of king Rudolf III of Welf. After that, it passed on to the Holy Roman Emperor as a semi-autonomous fief within his realms, like a component sub-state of the HRE. From the 12th century till the 14th, it became the stage of multiple dynastic struggles (amplified by the HRE's fragmentation after the interregnum of the middle 13th century), being eventually partitioned between multiple states including (but not limited to) the French County of Provence, the Dauphinais, the Duchy of Savoy, the Swiss Confederacy, the French Duchy of Burgundy, and the Free County of Burgundy right on the other side of the border in the HRE. The title of "King of Arles" continued to be used by the Holy Roman Emperor up until the dissolution of the empire at the hands of Napoleon Bonaparte, but as mere formal residue.
So, my question is... how can we prevent the fragmentation of Alpine Burgundy, preserving its status as an autonomous, territorialized kingdom under the proper rule of a single government?
Assuming this is indeed possible, how will the kingdom develop from there? What would its relationship with neighboring France, Germany, and Italy be like?
What sort of national identity would this kingdom adopt? Would it have to create an entirely new archetypical identity in order to balance out its numerous linguistic divisions?