  We study an extended 2 Higgs doublet model (2HDM) in which the Standard Model
(SM) Yukawa interactions are forbidden due to a global $U(1)^\prime$ symmetry,
but may arise via mixing with vector-like families. In this model, the
hierarchical structure of Yukawa couplings of quarks and leptons in the SM
arises from the heavy masses of the fourth and fifth vector-like families.
Within this model, we consider various non-standard contributions to the
electron and muon anomalous magnetic moments. We first consider the $W$
exchange at one-loop level, consistent with the $\mu \rightarrow e \gamma$
constraint, and show that it yields a negligible contribution to both electron
and muon anomalous magnetic moments. We then consider Higgs scalar exchange,
together with vector-like leptons, at one-loop level and show that it is
possible to have non-standard contributions to the electron and muon anomalous
magnetic moments within the $1\sigma$ constraint of certain experiments. We
present some benchmark points for both the muon and the electron anomalies,
together with some numerical scans around these points, which indicate the mass
regions of the Higgs scalars of the 2HDM in this scenario.
