We present $sim1-4$ resolution Very Large Array (VLA) observations of four CH$_3$OH $J_2-J_1$-$E$ 25~GHz transitions ($J$=3, 5, 8, 10) along with 1.3~cm continuum toward 20 regions of active massive star formation containing Extended Green Objects (EGOs), 14 of which we have previously studied with the VLA in the Class~I 44~GHz and Class~II 6.7~GHz maser lines (Cyganowski et al. 2009). Sixteen regions are detected in at least one 25~GHz line ($J$=5), with 13 of 16 exhibiting maser emission. In total, we report 34 new sites of CH$_3$OH maser emission and ten new sites of thermal CH$_3$OH emission, significantly increasing the number of 25~GHz Class I CH$_3$OH masers observed at high angular resolution. We identify probable or likely maser counterparts at 44~GHz for all 15 of the 25~GHz masers for which we have complementary data, providing further evidence that these masers trace similar physical conditions despite uncorrelated flux densities. The sites of thermal and maser emission of CH$_3$OH are both predominantly associated with the 4.5 $mu$m emission from the EGO, and the presence of thermal CH$_3$OH emission is accompanied by 1.3~cm continuum emission in 9 out of 10 cases. Of the 19 regions that exhibit 1.3~cm continuum emission, it is associated with the EGO in 16 cases (out of a total of 20 sites), 13 of which are new detections at 1.3~cm. Twelve of the 1.3~cm continuum sources are associated with 6.7~GHz maser emission and likely trace deeply-embedded massive protostars.
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