"not only that..."?

[dihen]

Is this incorrect?

"Not only that I [verb]..., but also...."

[Tdol]

Not only did/do/have/will I...

[dihen]

Maybe "It's not only that I [verb]... but also...." would be correct?

[Tdol]

That's possible:
It's not only that I feel disappointed, but also that many others do that leads me to ask for your resignation.

[dihen]

Is this grammatical correct, but unnatural?
`
It's not only [that he can sing] but also [that he can dance.]

[Philly]

Is this grammatical correct, but unnatural?
`
It's not only [that he can sing] but also [that he can dance.]

The structure is grammatical, but your choice of words (without further context) leads me to believe that you might not understand the usage of the structure.
.
I'd say this structure is normally used to give a justification or explanation for doing something.
.
So, on hearing your sentence, I'd expect that you want to justify your selection of him for the lead in a musical performance, for example. Your sentence cannot be used to simply state the fact that he can sing and dance.
.