Welding over an existing weld is common practice. Not sure if there are additional factors that need to be considered such as the type of welding technique (i.e. MIG, Arc) or the type of metal to be welded (e.g. aluminum).

I know American Welding Society has online discussion forums, perhaps look there for a better answer than mine.

You can weld over an existing weld, but its preferable to grind the old weld off and reweld if possible.

And reweld

I welded for 15 years, when I owned my farm and was building my greenhouses. Best welds are clean. I recommend , as do the others, that you grind away the old weld and start from a clean surface to assure the weld is solid. I was shocked when I saw the footage from the rollercoaster ride where the column and welds are imperfect and failed! Hair-raising!

and I know I'd want the one that failed removed as far as possible. First, it failed, meaning there was most likely something wrong with it. Second, a new weld will add mass and you'd have a large, lumpy weld. If it's out of sight, that wouldn't make much of a difference, but anything that will be seen needs to be ground down first.