Where might I find a frame for a Colt 1911?

You won't find a new Colt frame. Maybe a used one on Gunbroker or Gunsamerica. Brownells sells several other brands however.

You will not however, as stated, be able to assign your own serial number as once the frame is finished beyond 80% it is considered a firearm and will have a factory assigned serial number prior to sale.

Many many companies outsource major components of their guns. ARs recievers come from two or three sources

However Colt makes it's own frames

Try looking at Brownells or Gunbroker, other than that true Colt frame will be hard to come by

Personally I would go with a Caspian, better made and you can assign your own serial number

My One Of Theses Days gun is a Caspian made 1911A1 with a case hardened frame an engraved old style Colt royal blue slide with true ivory grips in .38 Super with the serial number BBQ 01

the frame is the part that has the serial number on it, that's why you are having a hard time finding one, if it was easy, any idiot can get all the parts on ebay, put one together, go to your house and shoot you. I would go to your local gun store and see what they can do for you, unless you don't have a gun card, and your not legal to have a gun, (I don't think you do, or are if you can't put a gun together yourself) than in that case I seriously hope you NEVER find one!