Ask LLOG: "What do you say (that) we …"

This morning's question:

I'm an ESL textbook editor in Korea, and a grammar dispute has come down to one question: is "What do you say that we get together tonight?" grammatical, with "that" included (vs. the more common zero-complementizer "What do you say we…")?

My understanding is "that" is simply optional here, not ungrammatical.

FWIW, my reaction is that both versions are acceptable, but both versions are grammatically opaque reductions of something like "What do you say (to the idea that) we get together tonight?". And my intuition, again FWIW, is that most people would reduce the beginning to the pronunciation conventionally written as "whaddaya say".

As usual, there's some discussion of related issues on the web, like this exchange about "What do you mean (that) it's wrong?".

The Cambridge Grammar of the English Language doesn't seem to have any discussion of "what do you say", but does consider simpler analogous cases like how come and how about (p. 909).

CGEL proposes that how come in How come the fridge is switched off ? "is best regarded as a compound interrogative word functioning as adjunct in a simple clause", derived by reduction and reanalysis from a source like "How does it come to be that the fridge is switched off?", noting that "it is impossible to insert that after come, a strong indication that the following NP (the fridge) has been reanalysed as subject of a main clause".

And CGEL suggests that how about in phrases like How about we leave the others until next week?, is an operator whose complement "can be an NP, a gerund-participial clause, or a tensed declarative clause", and whose "primary use is to put forward a suggestion". How about is presumably reduced and reanalyzed from a source like "How do you feel about the idea that we leave the others until next week?" — and the fact that about is preposition influences its wider range of uses, compared to how come.

What do you say has the same "put forward a suggestion" pragmatics as how about, but use with an NP requires to, as in What do you say to another drink?

These various word sequences are in plausibly in the middle of a historical process of reduction and reanalysis, so it's not surprising that they exhibit a variety of variable syntactic and phonological options. Myself, I agree with the judgment forbidding that in *How come that the fridge is switched off?, but I'm agnostic about that in What do you say (that) we get together tonight?.

COCA has 1111 examples of What do you say we, e.g.

What do you say we take this family reunion on the road?
What do you say we start some trouble?
what do you say we go get ourselves a new spaceship?

but only 5 examples of What do you say that we, e.g.

what do you say that we have dinner here together?
What do you say that we take a little breather?
what do you say that we quit our lousy jobs and go travel around the world?

So What do you say that is Out There, but apparently rare.