How can I change where Steam games save data?

In my Documents folder I have "\Klei\DoNotStarveTogether", "\My Games\Far Cry Primal", and "Square Enix\JustCause3" that are folders made automatically by the games. I'd like to move these folders to the same place. For Don't Starve Together I was able to go into the launch settings in steam and enter

'"-persistent_storage_root "C:\Users\USER\Documents\Game Saves\Klei"'

which successfully moved the save data.

Is there any way to do this for other games?

You can't do that, or rather Steam has no option that forces all games to save in the same directory.

Unfortunately or fortunately, each game creates and handles its own folders. Some games, like Don't Starve Together, have set up arguments to let the user decide where they'd like to store save data, but Steam has no universal way to change which folders are used by a game.

in similar fashion to what SteamMover does to your Steam games, you should be able to move the folder and setup a link to the new location, you would still need a shortcut (of sorts) in the original location.

You can use steam mover for this purpose just point its source to your mydocuments folder and destination to the new parent folder.

Or use the built in windows cmd "mklink" - Creates a symbolic link.

    MKLINK [[/D] | [/H] | [/J]] Link Target

    /D      Creates a directory symbolic link.  Default is a file
            symbolic link.
    /H      Creates a hard link instead of a symbolic link.
    /J      Creates a Directory Junction.
    Link    Specifies the new symbolic link name.
    Target  Specifies the path (relative or absolute) that the new link
            refers to.

Move the save folder to the new location eg d:\NEWsaveFolder

then at "command prompt" type

mklink /J c:\OLDsaveFolder d:\NEWsaveFolder

a special shortcut will be created in the original location to the new one and not take up any space.