Here's a rather late POD - ensuring King Aleksandar I Obrenović, after marrying Draga Mašin, does not get assassinated. In the event their marriage turned out childless, the plan was to declare Prince Mirko Dimitri Petrović-Njegoš of Montenegro as heir-presumptive and Crown Prince of Serbia, who was married to Natalija Konstantinović, granddaughter of Princess Anka Obrenović, an aunt of King Milan. Subverting Draga's brother Nikodije Lunjevica as to reduce the ire of the military and declaring Mirko as Crown Prince early on could probably help in at least preventing something akin to the May Coup happening, though it likely would not help in terms of popular opinion.
OTL, the path of the House of Petrović-Njegoš would see their exile from Montenegro confirmed in 1918 with its unity with Serbia and subsequent inclusion into Yugoslavia, Mirko passing away prior to that in March that year after divorcing his wife the year prior and moving to Vienna. King Nikola I would pass away in 1921, with the title of pretender to the throne falling to his eldest son Crown Prince Danilo Aleksandar Petrović-Njegoš, who would renounce his claims and headship of the royal house in favor of his nephew, Mirko's son Mihailo Petrović-Njegoš. TTL, if things somehow roughly followed the same timeline despite Mirko having become King of Serbia (and his long-standing thyroid issues don't cause him to pass away in 1918), Danilo may instead renounce his claims and pass them to Mirko instead (assuming the Montenegrin court supports the idea, seeing as they thought that the Petrović-Njegoš dynasty would be the ones to achieve the unification of Serbdom; otherwise, the only other brother Prince Petar Stefan Petrović-Njegoš would likely receive the crown).
Of course, this is more "The House of Petrović-Njegoš become the heads of Serbia" and less "Greater Serbia formed by Montenegro", but it's close enough!