I think that would work with one “that”.
“I didn’t know that employee was responsible”
… works for me, 'specially with a bit of stress -
“I didn’t know that employee was responsible”
When I taught a class about using Microsoft Word, I used “that that” in the Gettysburg Address as an example of a potential grammar issue that Word didn’t flag, while Word flags most other doubled words. I couldn’t think of other doubled words that are intentional like that.
When the owner of the Hare and Hounds pub received a new sign for his establishment, he promptly wrote the sign painter an angry letter: “The spaces between Hare and and and and and Hounds aren’t even!”
But his space bar kept getting stuck, so the spaces between Hare and and and and and and and and and and and and and and and and and Hounds weren’t even.
A sentence can be perfectly correct grammatically, yet still be confusing and/or aesthetically unappealing. I don’t think “that that” automatically puts a sentence into either of those categories, necessarily, but it’s something to watch out for.
I think that using words in quotes (or which should be in quotes) is bad form for this game. Otherwise you could have grammatical sentences like “The crazy bum said ‘rutabaga rutabaga rutabaga rutabaga’”, and thus claim that it’s grammatical to use the word “rutabaga” four times in a row.
“That that”, though? Sure. If it was good enough for Abe, it’s good enough for me.
The last paragraph of that article had a link to another article that also made for a fun read, in case you missed it. A couple gems from the article–
A sentence with 8 ‘thats’, first 5 and then 3 of them consecutive:
“I told him that that ‘that’ that that editor had deleted, was not that ‘that’ that I had marked.”
A punctuation puzzle:
It reminds us of a punctuation puzzle popularized by Flowers for Algernon , Daniel Keys’s 1966 science fiction novel, and Charly , a 1968 movie based on it:
that that is is that that is not is not is that it it is
Here’s one solution: That that is, is. That that is not, is not. Is that it? It is.
In the style guide that I follow, one is not supposed to suppress “thats.” So double “thats” occur fairly frequently.
Rather than it being correct to suppress an extra “that,” it is, rather, more colloquial.
I find that when two “thats” are used that way, I pronounce them slightly differently. (Including in my head as I read silently.)
The first is a more clipped, “th’t” or “thet,” and the second is a very slightly more expansive and clear “that.” The second one is also more emphasized.
It may not be ungrammatical, but I do often try to change my wording when I notice it, to avoid confusion. For example, if I were composing something like that quote in the Gettysburg Address, I would have written “…gave their lives so that nation might live.” Heck, I might autocorrect it in my head and thus misquote it.