A number of changes have been discussed and rejected multiple times, and sometimes discussed and ignored. Please review the below discussions before adding a new section for the parameter you would like to add. Each discussion is listed by most- to least-recent.

I would like |predecessor= and |successor= added
See: Add a space to input succeeding and preceding games if it is in a series, Three parameters suggestions, Add sequel and succeeded, Add "follows" and "follwed by" in videogame infobox template., Iterative games, Prequel and Sequel, GameSeries
I would like |website= added
See: Add a link to the website of the game, "Official Website" Field, No way to add a website., Template-protected edit request on 5 November 2020, Three parameters suggestions, add website parameter, website
I would like |based on= added
See: Template-protected edit request on 13 July 2020, How about a "Based on" parameter?
I would like |support status= added
See: Template-protected edit request on 31 May 2021, Early access date, Add field for end of life?, "Discontinued" date or similar for multiplayer/online games, Add new field for current status, Optional support stopped parameter wanted needed
I would like |infobox software parameter= added
See: Programming language, Optional Source Code Repo field, Add field for latest release version and date (as in Infobox software), Parameter suggestion: "size", Size parameter, Add license field?, Add a game version information, Programming language, missing fields
I would like |specific technical parameter= added
See: Addition of parameters, Parameters to the video game infobox, Addition of new optional parameters
I would like |other kind of parameter= added
See: Add Reception?, e.g. PEGI age ratings are missing from this info box, Budget field, Sound director parameter
I would like Wikidata to...
See: Release date (P577), Image property
I would like to refine how we treat a certain field, or even remove it
See: Staff precedence, "other_name" paramter, Propose adding Age Guide, Updating Computer Releases, Proposal on arcade fields (successful), On ending the practice of laundry listing dates..., Derivative copyrighted cover arts, Platform and Release Date fields, Guidelines for including Producer(s), Co-op, On staff in infobox, macOS in the infobox, Removal of the display parameter, Distributor (successful)