This film might have a storied history of alternative cuts, but there are two additional versions that I think might make for interesting viewing and projects.

The first, and simpler version, is a cut described on the IMDb page as being screen at the American Cinematheque. It seems credible enough of a version to have existed at some point. Essentially, it is a variation of the 1980 Special Edition but with the most regrettable aspects of that version reversed. The scene of Roy tearing up his yard for his sculpture and then entering his house through the kitchen window are both retained in this version, while the footage from the inside of the Mothership is excised. Essentially, it is a precursor to the 1998 Director’s Cut with a few of the trims and audio differences included in the 1980 cut. It is also easy to assume that the cutting around the Mothership interior is handled in a similar way to the 1998 version, without the extra footage of the original 1977 release (the shot of François Truffaut after Roy enters the ship is ever so slightly longer in the 1977 cut). This comparison explains it very well: https://www.movie-censorship.com/report.php?ID=973173

The running time of this version would likely be close if not identical to the original 1977 cut’s 135 minutes.

The second version is actually a precursor to the above, but would likely require a lot more effort (and in some cases, conjecture). This is a desire of mine to replicate the 1977 Dallas preview version before the last few trims were made for the initial 1977 first run version. I believe this version had John Williams’ score laid over it (and I use it for some of my conjectures here). All I can say for certain about this version at this point is this:

About 7-8 minutes longer than the first run version’s 135 minutes.
A small extension to the opening scene where LaComb outlines Laughlin’s job as a translator to him.
A potential extra shot or two during Roy’s driving scene (based on the soundtrack; there’s a small music jump in the final version).
Potentially the scene at the cookout where Roy sees the mountain shape in a jello salad. This scene is much further along in the edit than many other scenes on the Blu-Ray supplements, and notably included in the “Making of Close Encounters” documentary.
Roy’s star gazing on the deck built on the roof of his house. This scene has music to go along with it; it might be situated in between the army trucks being deployed, supported by a hard music cut in the official versions.
The infamous ‘Pinocchio’ ending. This wasn’t in every version of this cut, but I think it would be a necessary inclusion to give this version its own identity.

This might be impossible to create based on if there’s any footage that would have been included in this version that hasn’t been released. What I would like to know is if there is any information on this preview cut that might be missing from my list. There has been a great deal of writing on this film, and I recognize I could be missing any number of things.