Probably not a good option, but as a last resort if you have to and really want the car bad enough you might be able to get a builders type title.
Take in a bunch of receipts for various parts, engine, body parts, suspension parts etc.. and have the car inspected and titled as home built. Various states are easier or harder than others to get this done. Some of my old friends (hot rod builders, custom cars) used to do it alot. Some states are as easy as show a box of receipts (they may or may not check engine serail numbers) and if the lights all work and the brake pedal feels solid and correct you get a builders title for it. Other States may want to check each nut and bolt for correct torque and other nutty things and your better off to just travel to a different state.
If you go a custom built title route check into insureance first maybe. You might need to insure as a hot rod or other specailty class with a company that does show car type insurenace which some aren't much worse than any other insruance company and some are.
Back when I was more into everything and driving stuff so often I didn't bother with insureance, wasn't mandatory then. Now I still have a few ways to slip by (legally) for the occasional vehicle.
There are various ways, just rather you need to go to such extremes or feel it would be worthwhile or not is the question.
If nothing else get a dealers liscence, run on dealer tags and dealers lot insurance 
Big hassle and expense, but for some of us probably worthwhile! That is what I will be doing soon. Too many vehicles to insure each one and I can only drive one at a time anyway. So one for wife, one for me, on normal insurance registered and such. All the rest will be drivin on dealer plates. No title fees, No personal property taxes, No registration ($25 or more each), No insurance per vehicle ($100-$150 each), just slap a tag on anything and go and perfectly legal! Cuts currant insurance bill by about $600 per year, cost is about $1,000 per year for dealer insurance and $200 to state for liscence and tags. So I only pay out about $600 more per year than now (actually alot less since I won't be payng registrations and other stuff also), drive anything anytime, and buy wholesale from other dealers and auctions.
For me I figure this is worthwhile. Since I have over 30 vehicles already, most are ready to roll or only need very minor things like batteries, I can drive a different car everyday of the month. Anything I build I won't have to worry about titles and inspections for awhile. And If I make about $400 profit selling a car or 2 durring the year I actually break even with what I am paying out now anyway.
The headache of doing a little paper work for the dealer lisence each year is offset by all the headaches I get rid of with individul car registrations, inspections, etc...
Not an option for everyone, but worth it for some of us
