Great question!

(credit to HotbrownDoubleDouble for the map)

So, when Aegon I started up, Harren Kingdom of the Isles and Rivers was clearly on the offensive:

“…but the most belligerent kings of Aegon’s time were the two whose realms lay closest to Dragonstone, Harren the Black and Argilac the Arrogant. From their great citadel Storm’s End, the Storm Kings of House Durrandon had once ruled the eastern half of Westeros from Cape Wrath to the Bay of Crabs, but their powers had been dwindling for centuries. The Kings of the Reach had nibbled at their domains from the west, the Dornishmen harassed them from the south, and Harren the Black and his ironmen had pushed them from the Trident and the lands north of the Blackwater Rush…
North of the Blackwater, the riverlands were ruled by the bloody hand of Harren the Black of House Hoare, King of the Isles and the Rivers. Harren’s ironborn grandsire, Harwyn Hardhand, had taken the Trident from Argilac’s grandsire, Arrec, whose own forebears had thrown down the last of the river kings centuries earlier. Harren’s father had extended his domains east to Duskendale and Rosby. Harren himself had devoted most of his long reign, close on forty years, to building a gigantic castle beside the Gods Eye, but with Harrenhal at last nearing completion, the ironborn were soon free to seek fresh conquests. No king in Westeros was more feared than Black Harren, whose cruelty had become legendary all through the Seven Kingdoms.”

Hence why, when Aegon started, Argilac Durrandon and Sharra Arryn both approached Aegon about an anti-Harren alliance, with Argilac hoping to “establish the Targaryens along the Blackwater as a buffer between his own lands and those of Harren the Black,” and Sharra looking for “all the lands east of the Green Fork of the Trident for the Vale’s support against Black Harren.” Although if you want a good sense of how crab-bucket politics the Great Game could get, consider that Princess Meria of Dorne approached Aegon with a plan to gang up on the Stormlands…So you have two dynamics at once: a bunch of players wanting to pounce on the declining Stormlands to get what they can while they can, but also a number of players seeing the Ironborn as the new threat that needs to be jumped on with both feet lest they win the Great Game. 

With no Aegon, I would imagine Harren would keep pushing south as the Durrandons ran out of steam…up until a crucial point, probably during a siege of Storm’s End. Then you’d see a couple things happen: first, the Vale would launch an invasion of the eastern Riverlands to “liberate their Andal brethren from the heathens.” Second, the Rock and the Reach will announce that “Harren the Black is a threat to all of Westeros,” and promptly invade the Riverlands from the west and the south…although maybe they’ll do something weird like launching a joint naval invasion of the Iron Islands at the same time. Third, Harren will be forced to pull back, and everything turns into a blood bath in the Riverlands. 

And the Great Game would shift, likely with the Iron Islands reduced, the Riverlands divided (probably with the Westerlands grabbing Riverrun and the Trident, the Reach trying to grab everything from Stony Sept to Lord Harroway’s Town to Maidenpool and overreaching, and the Arryns fighting the Reachermen for Crackclaw Point and the Westermen for the Ruby Ford), and everything in chaos. The Durrandons might luck out with a rump state against fierce Dornish pressure – although who knows, maybe a Gardener decides to get their own back for Garth X by burning Sunspear or something, and that gives them enough breathing room to rebuild their fortunes. Oh and I’m sure that a Gardener will start talking about “saving the Stormlands from the Dornish” and the claims of Garth VII’s daughters. 

So yeah, there’s plenty of ways to redraw the map to build multi-national states – the problem is the Great Game makes all of this unstable as hell, because it’s designed to prevent anyone from winning.