Well, split with Lithuania is possible - in 1389 Vytautas joint Teutonic crusade against Skirgaila, supported by Poles and Jogaila, and besieged Vilnius. Jogaila managed to convince him to switch sides offering him stewardship of Lithuania with a title of a grand duke (Jogaila remaind supreme duke). But secret negotiations might fail, Vilnius might fall, and Vytautas becomes the ruler of Lithuania, although I doubt if he would have managed to control of all the country.
Other possibility is the crisis in 1429-1430, when Sigismund of Louxemburg proposed to make Lithuania a kingdom with Vytautas as full king (he wanted to break Polish-Lithuanian union). Jogaila originally agreed, tthen changed his mind. Poles intercepted imperial envoys with crown for Vytautas who was also offered an anti-Polish alliance with the Teutonic Order and Sigismund. The whole plan failed, also thanks to popr Martin V who refused to agree for Vytautas' coronation because he had not been asked before.