Here are some things that need to be part of the story:
1. The 4 Founders are actually 4 Bastards of major Houses.
a. Godric Gryffin (Godric Gryffindor) is a bastard of House Lannister and Connington (Lion and Gryffin symbol)
b. Sylas Snake (Salazar Slytherin) is a bastard of House Lynderly (House Lynderly sigil is a snake)
c. Rowena Raven (Rowena Ravenclaw) is a bastard of House Corbray (House Corbray sigil has a raven)
d. Henrietta Hedge (Helga Hufflepuff) is a bastard of House Lydden (House Lydden sigil has a badger)
2. The first students at the school are actually children of lords who will eventually make up the Pureblood Sacred Twenty-Eight.
Example 1: The Olivander family is actually House Rowan of the Reach who become the first Wandmakers.
3. Find a way to bring magical creatures life House-Elves and Goblins into the story.
Example 1: Goblins were created in Old Valyria and were the creators of Valyrian Steel. They now secretly work for the Iron Bank minting coins.
4. Find a way to make travel easier since the Hogwarts Express doesn't exist in this world.
Example 1: Harrenhal has the Hall of a Hundred Hearths which would make it great for Floo Travel.
5. Thanks to magic Harrentown prospers to become an actual city like Oldtown or King's Landing.
Example 1: Gringotts bank is made in Harrentown
Example 2: Many Guilds are built.
Example 3: The first Hospital is also created.