His ultimate plan was world domination.
The Dark Lord’s ultimate plan was for wizards to rule over the Muggles. He never specifically limits this to the United Kingdom, and it seems most likely that he would want this to eventually reach the entire world rather than be confined to one region.
“For years he talked of the Dark Lord, who was going to bring the wizards out of hiding to rule the Muggles and the Muggle-borns … and when he was sixteen years old, Master Regulus joined the Dark Lord.”
- Harry Potter and the Deathly Hallows, Chapter 10 (Kreacher’s Tale)
Furthermore, J.K. Rowling says in an interview that the Dark Lord eventually did plan on taking over the whole world, though he planned to gain domination over Europe to begin with.
Question: How does the Dark Lord affect American wizards and witches?
J.K. Rowling responds: He affects everyone, but his plan is European domination first.
- Scholastic.com interview (October 16, 2000)
So yes, the Dark Lord ultimately planned to have wizards in power over the entire world, ruling over Muggles openly.