Your car and other drivers.

[RVGRINGO]

First, you would have to move to Mexico and qualify for an FM3 Visa by proving a Mexican address and showing sufficient income/resources to support yourself in Mexico. Next, you would have to gain the permission of Immigration to work at a 'lucritive' job. Beyond that, would be the necessary government permits for a taxi business and figuring out how to survive (perhaps literally) the ire of the local taxi unions.
Buying a car is the easy part, once you have an FM3 and an address, but I have no idea how you would obtain a 'sitio,' a taxi stand to operate your business. That is strictly controlled and you can't just pick up people at airports, etc.
I think you might consider moving to Mexico first and then investigate your options. I assume you are fluent in Spanish to even consider your idea of a taxi business.

[thefieldisgreen]

Yes I am fluent in Spanish. So I was a little puzzled by your explanation of the requirements to buy a car in Mexico. I considered the processed of a Mexican buying a car in the US, a Mexican would only need ID nothing more. Now I Real-estate is very easy to buy in Mexico it can practically been done all online from the United States, surely buying a car in Mexico would not be more complicated. So I went to the local Mexican Consulate to ask to same question. They assured me that the only requirement, for an American, to buy a car in Mexico that is going to stay in Mexico is ID (Passport), and money. So I am confused why you insist that I need a FM3 to buy a car in Mexico, (maybe I misunderstood what you wrote.) I would be very grateful if you could clear the matter up. Thank you for your attention.

[RVGRINGO]

Buying a car would only require a Passport and money; that is correct. Consulates are notorious for incomplete and sometimes incorrect information. This seems to be one of those cases because, at least in Jalisco, you must prove your address in order to register the vehicle. For foreigners, that means an FM3 or FM2, as was required when we purchased a car in Guadalajara. The dealer requested our documents, took care of the registration and delivered the car to our home two days later.

[thefieldisgreen]

Thank you very much for your reply. In the US one person can have the title of the car and it may be registered with another name. Could I not buy the car, have the title in my name and have it registered in the name of a friend who is Mexican?

[RVGRINGO]

No, no, no. To temporarily import a vehicle to Mexico, everything must match, including the name on the credit card you use to post the bond for the car.
It is also important to know that a Mexican cannot, not even a valet, drive your car without you in the passenger seat. If he injures someone or does property damage, your violation of that rule will cause the car to be permanently confiscated and may land you in jail, or worse. Only an immediate family member may drive your car with an 'importada temporal'(and they had better be able to prove it and also be listed on your insurance policy. Another expat with the same migratory status may also drive it with a letter of authorization & insurance plus a copy of your Immigration document showing identical signatures.
Forget 'what happens in the USA'. You will be in Mexico and things are very different.

[makaloco]

Thefieldisgreen: You're talking about buying and registering cars in Mexico, right? Try searching "ley tránsito Oaxaca" or "reglamento tránsito Oaxaca", which should get you to the legal requirements for your state. If the car(s) will be used in the taxi business, there are likely to be different rules than for privately owned and operated vehicles. Or wait until you get there and visit the local traffic department. As for the FM3, you will need one anyhow to start a business. FWIW, in my state (Baja California Sur), like RVGringo's, an FM3 or FM2 is required for car registration and to get a driver's license. And you can't drive a BCS-plated car with a foreign license, though in other states, apparently this is okay. So check the laws for your area.