GEO debuffs don't overwrite their corresponding buffs:
And exist alongside the corresponding debuffs:
Similarly, many GEO debuffs are unique status:
As a result, there are interesting things that can happen! For example, Geo/Indi-Slow and Slow (white magic) are applicable at the same time (they are different status effects).
Also, all buffs appear to stack with their similar counterparts:
Debuffs can't be erased:
Also note that the Geomancer in the picture is level 65 with 4 combined skill vs. level 99 players, so that doesn't seem to have any bearing on whether or not the GEO aura sticks.
Conclusions:
Geomancer's Def Down effect should be stackable as I've previously suggested.
Unexpectedly, GEO's slow effect stacks which could lead to interesting strategies with Slow II / Indi or Geo-Slow / Elegy.