Factory based on input variable

I read some tutorials about a the factory an abstract factory pattern and saw some examples of it. In one of the tutorials i read that the factory pattern could replace major "if" or "switch case" statements and follows the open/closed (solid) principles.

In one of my projects a have a huge "switch case" which i wanna replace by a(n) (abstract) factory. It's already interface based so implementing an factory shouldn't be that difficult but in all the examples i read in tutorials the factory produced a single concrete type based on configuration. Can anyone point me in the right direction how to implement a factory that could produce multiple types based on an enum that follows the Solid principles an replaces the large "switch case"....or am I misinformed and is the "switch case" moved to the factory?