I do do that

[tufguy]

We say. "I do eat that" or "I did eat that". Can we say "He does do that" or "I do do that"?

 

[emsr2d2]

All four of your examples are grammatically correct and could be used in the right context.

 

[tedmc]

Yes, you can.
You use does/do/did in front of a verb for emphasis.

not a teacher

 

[MikeNewYork]

I would try very hard to rephrase a sentence before using "do do".