I don't get into the fixed-gear stuff much. But I was thinking that it wasn't uncommon to take an old road frame, and grind off all the little doohickeys that hold cables and derailleurs and such, to have a cleaner slicker frame. If that's the case with your bike, it might be easier to go pick up another vintage multi-speed bike that hasn't been converted.

Generally, you'll have a wider gear range with multiple gears in the back, so that would be the preferred arrangement if you just convert the front or rear.

It is possible to build 3-speed (or more) hubs into a new wheel, but I don't know what hub widths are available, or what other issues might come up there.