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

Explaining The Muon $g-2$ Anomaly and New CDF II W-Boson Mass in the Framework of (Extra)Ordinary Gauge Mediation