All in one feet are quite common (and sometimes surprising complex) on late 19C/early 20C glass from Bohemia and possibly the UK, don't know about US glass. I have at least four pieces. See both pages
here and also
here.
I'm not suggesting your vase is Bohemian BTW
John Walsh Walsh registered several designs for flower holder sets - vases linked by glass or metal chains, ribbons or arches in 1906-1909. I think arches, whatever they were made of, can be ruled out because of the hooks, but the other three options are all possible. (Gulliver p284-285) Your vase doesn't match any of the designs illustrated but the principle is the same.