For me, it's more like the other way around.
Rather than adding other properties to a 'Joeverse', I have a Universe that I use, and then GI Joe was added to it.
My Universe is basically "Aliens-like" in outer-space, and "Robocop-like" on Earth. The universes from those movies are blended together to form the Universe I use. The Terminator universe is also a part of it, but obviously with some differences. Such as the immanent danger from the "machines" is further off in to the future than it was in the movies, but it is still there.
I have droids in my Universe. Everything from V.I.N.Cent (Black Hole) and Star Wars droids, to B.A.T.s (
very early Terminator models) and synthetics such as Ash and Bishop from the "Alien" movies. And of course USCM ED-209 units.
The USCM exists as it did in "Aliens", and their primary territory is outer-space.
On Earth there is the main military, or Global Earth Defense Force (PTE). Each country has their own branch of the same military force. Such as the United States has the USGEDF, Japan has the JGEDF, the United Kingdom has the UKGEDF, and so on.
GI Joe is a small Special Forces unit within the USGEDF, consisting of two 5-man squads, a commanding officer, and a small support team. The support team consists of tech specialists, logistics support, and various droids and synthetics. Liaisons to each other military organization, as well as corporate liaisons, are also in place, but not really members of the GI Joe team.
While the GEDF deals primarily with Earth issues, and the USCM deals with primarily outer-space issues, GI Joe is used where ever they are needed, working with all of the other military forces, depending on where the assignment is.
Though I have not created any yet, there is always the possibility that other countries have their own version of GI Joe within their own military forces.
Cobra exists as primarily a "hostile corporation", with a substantial private military (as is common amongst high level corporations).
Their primary goal is to take over other corporations and have been known to resort to physical take-overs, if normal business methods don't work. Because of their influence (and fear) they always manage to avoid any form of prosecution and tend to suffer no repercussions from their actions. Because of this, the GEDF can, officially, do nothing against them. Unofficially, GI Joe has gone in to many situations involving Cobra, and halted their activities, covertly.
Cobra knows exactly who is interfering with their plans, but they haven't been able to provide ample proof, so there is nothing, legally, that they can do against GI Joe. They try to avoid large military operations, or strikes against GI Joe, for fear that it would give the GEDF (and possibly the USCM) sufficient reason to launch counter-strikes against their company.
Cobra has been known to do "dirty work" for other corporations, such as Weyland-Yutani, who want to keep their own involvement to a minimum. They also purchase equipment from other companies, like weapons from MARS, and combat droids (BATs) from Hyperdyne Systems (created by the merger of Cyberdyne and OCP), all of which helps to keep their inter-corporate influences strong.
I use pretty much anything 1:18 scale in my Universe. While most Star Wars tech exists, and is used, Jedi and Sith aren't much of a part of it. One or two Sith have appeared, but were dealt with by various super heroes, and were therefore classified as super villains. A few Jedi exist, but pretty much live like "A New Hope" Obi Wan did. Keeping to themselves, and not using their powers in public at all.
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"Now I am somewhere I am not supposed to be,
and I can see things I never really should've seen,
and now I know why, and now I know why...
things aren't as pretty... on the inside"