Can I re-distill Cheap Vodka (like Taaka, etc), and end up with a smoothie like Tito's or Absolut?

Tito's fine Vodka is distilled 6 times.. does that mean I can take a cheap vodka and send it thru a distilling process and make something just as smooth? What would happen if I took a half gallon of Taaka and distilled it 7 or 8 times? Inquiry minds want to know...