Yes, you can get them in a "standard" thickness as well as a "slim" or "CCW" thickness with is generally very thin.
There are some out there that are thicker, or than have palm swells and slightly different profiles that will feel thick....though I can't specifically point you in the direction of a "thick" 1911 grip.
Many of the custom made wood grips can be had "thick" by special request...but you're likely looking at $50+ for the pair.
If you look in my "22/45 mods, my way" thread you'll find measurements of my factory 22/45 grip, as well as the hogue 1911 grip I installed. I'll tell you it fills the hand MUCH better!