The Civilization forum has revealed that there is a way to enable team multiplayer on Civilization VI, something the base game is lacking, although this does mean altering game files in order to do this.
Team multiplayer is there in the files of the game, but is disabled for whatever reason. There is a way to enable it, however, by editing line 1134 "playerEntry.TeamPullDown:SetHide(true)" to "(false)". This can be found in "C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization VI\Base\Assets\UI\FrontEnd\Multiplayer\StagingRoom.lua". It doesn't work amazingly however, as Civilizations can't share research or technologies and areas uncovered by players can't be seen either.
What is important to note is that Firaxis Games obviously put it in there, as evident by the files, but there may be a very important reason it is disabled, so doing this may crash the game and should be done at your own risk. Those that are patient enough to wait may even find team multiplayer coming to the game soon anyway, so we wouldn't totally recommend tampering with the game. Do you miss team multiplayer?