  We construct new semi-realistic Type IIB flux vacua on $Z_2\times Z_2$
orientifolds with three- and four- Standard Model (SM) families and up to three
units of quantized flux. The open-string sector is comprised of magnetized
D-branes and is T-dual to supersymmetric intersecting D6-brane constructions.
The SM sector contains magnetized D9-branes with negative D3-brane charge
contribution. There are large classes of such models and we present explicit
constructions for representative ones. In addition to models with one and two
units of quantized flux, we also construct the first three- and four-family
Standard-like models with supersymmetric fluxes, i.e. comprising three units of
quantized flux. Supergravity fluxes are due to the self-dual NS-NS and R-R
three-form field strength and they fix the toroidal complex structure moduli
and the dilaton. The supersymmetry conditions for the D-brane sector fix in
some models all three toroidal K\"ahler moduli. We also provide examples where
toroidal K\" ahler moduli are fixed by strong gauge dynamics on the ``hidden
sector'' D7-brane. Most of the models possess Higgs doublet pairs with Yukawa
couplings that can generate masses for quarks and leptons. The models have
(mainly right-) chiral exotics.
