There's 2 different things to consider, the feds and the states. The federal gov't doesn't do vehicle registrations, so more often than not, if state requirements are satisfied you can have a car registered. EPA and DOT requirements are pretty strict, bascially any engine swap, or any engine modifications, as well as bumper and headlight mods cannot change emissions or saftey of the vehicle, and sometimes the feds require this is proven.
I have seen vehicles imported in pieces then reassembled and titled without going through the federalization process. Is it legal? From a state persepctive it is, however EPA and DOT will tell you otherwise.
The federalization process is VERY expensive, and quite often you will pay the cost of the car to get it done.
So what do you do? The least expensive way to get what you want is to make it yourself, however with the caveat that any engine transplants or swaps also need to meet federal requirements, which puts you in the same boat as importing the damned car you wanted in the first place.
However the reality is that once it's registered it's unlikely the EPA will show up at your door wanting paperwork.