It's hard for me to envision a Mongol Empire honestly especially one of this size. Now I'm not saying a Mongol State isn't possible although it's would be difficult trying to unite and lead so many tribes and peoples all with their own cultural norms, religions or variations on religions, laws, and distinct identities some of them not Mongol at all but belonging to related and alternative tribes. I think the best chance of forming a Mongol Nation is in the early 1200's with a Chief Qara Khitai sources identify as Jamukha. He was in the process of solidifying power among the various factions at about that time creating a confederation of 13 tribes including Tatars, Naimans, Merkit, Jadaran, and Taichuud, probably the most powerful groups on the steppe at that time. Collectively these groups came together and declared Jamukha to be their Gur Khan which means something like Universal Leader, basically an elected king. Just as it looked like the Mongols and their allies were on the brink of military expansion a civil war broke out with a potential usurper named Temujin, sadly they both died at a confrontation called the Battle of the Thirteen Sides. The tribes and sub-tribes quickly started bickering among themselves and fell into chaos. They were quickly absorbed by a coalition of the more sedentary states around them made of Jin, Western Xia, and Qara Khitai. Although amazingly the Eastern Khitan tribes managed to resist this annexation uniting under their cultural identity and memory of their former Empire and created small kingdom that would eventually invade and conquer Korea.
So assuming that Jamukha survives the battle that took his life and was victorious I imagine he would quickly bring the rebelling tribes into line with the new order, placing his own people in charge of those regions or groups. With his rival dead or exiled it would be fairly easy to secure his own power base and turn the Confederacy into a Hereditary Kingdom modeled on his allies in the Western Khitan and enact tribute and taxes from his new subjects. It would be hard to miss the fact that the north is wide open for settlement by this formerly tribal peoples, only needing to find and follow the rivers for the best and most fertile land. Not to mention the riches of the forests provided by hunting and trapping, Mongolian Siberia. As for the south and west if the Military Elite are patient they can wait for disunity and rebellion in neighboring states and break away whatever chunks they can hold onto and incorporate into their new Mongol Nation and identity. Although this tactic could be used against them as well. Cards played right though they might be able to expand near to Kwarezm or Song. Though it would be nearly impossible to hold that territory for long. They'd also be limited by the sheer size and variety of terrain in Asia deserts, mountain ranges, tundra, grasslands, swamps, and forests. Not to mention all the climate and weather conditions in those areas no army can prepare for everything.
All in all a Mongol Kingdom or State is entirely possible the leader of this state might even call himself an Emperor in the tradition of the Song influenced nations around him but this would be an Empire in name only even at its strongest. I see it more a regional power with deep rivalries among its neighbors navigating a landscape of shifting alliances and cut throat politics. It's unique history and cultural identity will make it stand out from the other East Asian states though and could have lots of impact locally. Just another nation state created in the wake of the final collapse of the Han dominated mega states of the past.