I read a study by Tomasz Campa (I don’t know if it has an the online version or not, I read in the paper version)
so, during the so-called "first War for the Polish Succession"
https://ru.wikipedia.org/wiki/Австрийская_интервенция_в_Польше_(1587—1588) one curious episode happened which had certain chances to change history
On November 8 - 17, 1587, the congress of the gentry and magnates of the Grand Duchy of Lithuania gathered in Vilnius, where they decided on "what to do and whom to support in a situation when the Convocation Sejm elected two competing kings at the same time". The congress very clearly showed that, unlike the Polish gentry, the nobility and the magnates in Lithuania were on the side of Maximilian, not Sigismund (this fact is clearly shown by that only 13 votes were given for Sigismund III, while all the rest were for Maximilian). Also, to help Maximilian's case, the nobility of the Grand Duchy of Lithuania agreed with Moscow that Fyodor I of Russia would support Maximilian’s candidacy when he was elected to the throne (to which their letter received Fyodor’s reply, in which he congratulated Maximilian on his election and promised to keep the peace)
According to the decision of the congress, the participants, headed by representatives of the Nesvizh line of the Radziwills, sent Maximilian a letter in which they proposed to lift the siege of Krakow (which they considered doomed to fail) and arrive to Vilnius, since the nobility and magnates of Lithuania had already elected him as their monarch, and as soon as he arrived in Vilnius, he would be crowned as Grand Duke of Lithuania, and with a Lithuanian crown and army, he then will be able to fight for the Polish crown.
in OTL, Maximilian, having received this letter in November 1587, ignored it, since he still hoped to take Krakow (by the end of November, he was convinced that it was in vain and retreated south)
Alternate scenario - Maximilian accepts this offer, lifts the siege of Krakow and goes to Vilnius with his army. In December 1587, in Vilnius, Maximilian is crowned Grand Duke of Lithuania. The war between him and Sigismund III continues, but Maximilian here has the army of the Grand Duchy of Lithuania by his side. The civil war lasts until 1589. Neither Maximilian fails to defeat Sigismund's supporters in Poland, nor Sigismund fails to defeat Maximilian's supporters in Lithuania.
In March 1589 a peace treaty is concluded, according to which, the Rzeczpospolita ceases to exist
Maximilian recognizes Sigismund as king of Poland and renounces, respectively, the title of King of Poland.
Sigismund recognizes Maximilian as the Grand Duke of Lithuania and renounces, accordingly, the claim to the Lithuanian crown.
Respectively, instead of the Vasa-ruled Polish-Lithuanian Commonwealth of OTL, Poland turns out to be Vasa-ruled and the Grand Duchy of Lithuania is ruled by the Habsburgs.