  The SUSY contributions $\Delta a_\mu$ to muon $g-2$ anomaly can not even
reach $3\sigma$ in ordinary gauge mediated SUSY breaking (GMSB) scenarios
because of the strong correlations between the colored sparticle masses and the
uncolored EW sparticle masses. An interesting extension to GMSB is the
(Extra)Ordinary Gauge Mediation (EOGM), which can relax the correlations
between squarks and sleptons with non-universal choices for $N_{eff,3}$ and
$N_{eff,2}$. We find that EOGM scenarios with $N_{eff,3}\ll N_{eff,2}$ can
explain the muon $g-2$ anomaly within $3\sigma$ range, however can not explain
the new W-boson mass by CDF II. We also propose to extend EOGM with additional
adjoint $\Sigma_8$ and $\Sigma_3$ messengers at a high scale of order
$1.0\times 10^{14}$ GeV, which can shift the gauge coupling unification scale
to the string scale. Such EOGM extension scenarios with adjoint messengers
could spoil the unwanted gaugino mass ratios and give large SUSY contributions
to $\Delta a_\mu$ for $N_{eff,3}\ll N_{eff,2}$, which can explain the muon
$g-2$ anomaly up to $1\sigma$. Besides, because of the large messenger scale of
order $1.0\times 10^{14}$ GeV, such scenarios will in general lead to large
$|A_t|$ at the EW scale, which can accommodate the 125 GeV Higgs easily and
possibly lead to smaller EWFT as well as BGFT. We discuss the possibility to
explain the new CDF II W-boson mass in the GMSB-type framework. We find that
SUSY contributions can marginally account for the new W-boson mass in the
region with sleptons and wino both being light.
