Additive & Subtractive Printing???

It is my understanding that 3D printing has existed since as early as the 70's, but in the earlier stages it was a subtractive process whereby material was removed from a solid block or something, but later became additive to use only the material that is needed and waste nothing. I was wondering if there were any printers out there that are the best of both worlds?

For example an additive printer that draws the object, but makes it a slight bit more bulky than the final product will be, and then shave away the rest? I figured with extreme overhangs and things that even the best additive printers have difficulty with it might be helpful if it simply added extra padding, have it dry, and then remove it to create a more perfect model?