Many. There are no definitions for what is a "number", so people just name stuff "number" if they feel like it. Later 19th century-early 20th century had people came up with all sorts of different algebra that they keep calling "numbers". They kind of stop now and calling these new stuff like that "algebra" instead, but historical names remains for old things.

Hyperreal, surreal extends the real. Surcomplex is complex version of surreal.

Dual complex, split complex, bicomplex, Grassman numbers all have different algebraic structure.

p-adic number is like numbers that you're allowed to write an infinite digits to the left. Different analytical structure, but not algebraically.