Huang, Katz and Klemm conjectured that the generating series (with fixed based class) of Pandharipande-Thomas invariants of an elliptic Calabi-Yau threefold are Jacobi forms. I will explain joint work with Maximilian Schimpf in which we extend the conjecture to elliptically fibered threefolds, which are not necessarily Calabi-Yau. The price to pay is that one obtains quasi-Jacobi forms. The quasi-part is controlled by two holomorphic anomaly equations. I will discuss evidence for the conjecture, in particular in the case of K3xP1, where it relates to holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface.