OpenGL versatile for older computers?

I was thinking of making a game engine with OpenGL, but I was wondering if its possible to make it have really high graphics and settings for modern computers, but still be able to be downgraded (like in options or something) for older computers.

That is definitely possible. Things like having different screen resolutions is really easy to implement, but if you want to take advantage of newer OpenGL versions on modern graphic cards while still having your engine being able to run on old computers, you have to implement different code paths for different versions of OpenGL.

You do that by checking the GL version

and for extensions, well, you check if the extension is in the list or not.