You can get six 9’s, and it has been done, back in the 1950s.
A bit more than six 9’s may be possible, but there is no real reason anyone wants to do that.
Wanting absolutely infinitely pure gold, would tend to be a misunderstanding, an obsession, and/or an unrealistic theoretical/philosophical/alchemical notion.
Usually people intentionally mix other metal(s) with gold, because pure gold is so soft, and they want certain colors, and/or to have more metal for less cost per weight.
24K (five 9’s) is the most pure that people generally (if not always) make or sell.
@Hawaii_Jake Gold is quite heavy, and when one melts it into bars, other stuff tends to get worked out.