Multiplicities of Monomial Space Curves with Non-Noetherian Symbolic Blowups

We study the multiplicities of space monomial curves with non-Noetherian symbolic blowups. We extend the celebrated examples of Goto, Nishida, and Watanabe, as well as introduce a new family of examples. In particular, there are such curves with multiplicity 11, and curves having any given multiplicity over 25 (with 12 possible exceptions).