Is “more additional” bad grammar?

Use either "more" or "additional". Do not use both.

Eh, not really. As everyone else is saying, it does sound redundant, but for whatever reason, it's one of those things that flows nicely despite not being technically correct

The answers from Dan and A.J. show a deeper understanding of the possible correct usage.

Yes, it's like saying " more more."

YES!!! you don't need additional. It is a style choice to use either 'more' (the correct option) or the second 'additional.' Use 'additional' in a financial statement, or when talking to a policeman.. Keep it simple.

No, as in, we're building 3 more additional classrooms.

Normally, it is redundant, more meaning the same as additional. It is possible to have a special case of "additional" as a category and "more" the added quantity of it. They offered more additional services and fewer base services.

Using "Very very" is also redundant.

Add, in reviewing the precise content, "more additional" is valid in the special case.

seek a recount --- would give them more additional votes than their opponent

The original counts are assumed to be missing valid votes

Each candidate is expected to get "additional votes" as a category of votes.

More than the other candidate of the additional votes is valid.

No in this sentence that is the correct usage, as both candidates can possibly get additional votes, so it matters who get more number of additional votes.

Makes no sense. They’re synonymous.

No, it is redundant. "more" and "additional" mean the same thing.