EbDim7
So I’m learning some Christmas songs for a Christmas Party. Frosty the Snowman is one. The version I’m using has an Ebdim7 (see below). It’s an easy transition from the D before it, so no problem.
Coincidently yesterday someone told me that chord shape can be moved up 3 frets and it is still Ebdim7 (inversion). Then move it up 3 more frets and still Ebdim7 (different inversion) and so on.
I think that is really cool.
My question is: Are there any other chords this or something similar can be done with? I haven’t found any yet.

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@David Lieder I tried the D diminished, D augment, and G in that spot and liked them all. I guess it depends on how jazzy you want it to sound. I'm partial to the D dim. :D