Well I have looked into this a bit and the answer is yes and no .
Could you buy parts and just put them together ?
Perhaps but in the end it may cost you more than it would to buy a lower price end gun that can be very good , for instance a RIA or Charles Daly 1911 or even the basic Springfield can be had at reasonable prices .
You could say call up Caspian "http://www.caspianarms.com/index.php" and buy a frame , slide and barrel all together and ask them to make sure they mate up correctly but this alone would get you in the $500+ range , then one of the most importatant areas of the weapon are the fire control parts needs to be fitted for safety reasons "Hammer , Sear , Disconnector" if these are incorrectly fitted you could have a dangerous gun that could go full auto on you .
You can purchase kits from Cylinder n Slide http://www.cylinder-slide.com/
and the parts are all set but these will cost over a $100 Things like triggers and mainsprings , mainspring housings , grip safeties , thumb safeties , slide stops should all either drop in or be fit with a touch of sanding by hand with wet/dry .
has almost everything you need listed for sale , go there and try adding up all the parts costs and see what you get .
All in all unless you truely want a custome gun I don't think it's worth it .
Heck if you just want a very nice accurate , reliable 1911 shoot me a PM and I have a Charles Daly full sized with a 5 inch barrel in blue I am selling for $400 . IT has a sweet trigger pull straight from the factory and yes she feeds hollow points .
I have a couple of Pics if you're interested .