You know, this seems obvious in retrospective but I just finally figured out what the Arm Doppelganger was doing in Part 2, though might be late to the party.
So Mr. C had a very elaborate plan to stop Cooper from replacing him as we know, manufacturing Dougie somehow in 1997, getting hitmen to try and murder Dougie , etc. But the Arm Doppelganger in Part 3 was totally working with Mr. C. I don't know why I didn't realize the Arm Doppelganger was working with him, as he was directly blocking Cooper from exiting the Lodge to where Mr. C was and instead sent him flying through space, then through the box which Mr. C had set up as we know now. The box I think was supposed to be a way to send him to the area in the Purple Ocean place, since otherwise he may have been sent to New York instead, but the box seems it was set-up to sort of 'catch' people going through worlds, it catches Cooper and then sends him to the Purple Place. It's also shown this connection is intentional as The Experiment/Mother later comes through from the Purple Place side into the box.
The rest is pretty much known, and this seems obvious so I bet some others caught it, but for some reason up until now I hadn't 100% put together that the Arm Doppelganger must've been working with Mr. C and the Box must've been to specifically been placed as it's some place between worlds where the Waiting Room, our world, and the Purple Place interchange it seems. However, if the Arm Doppelganger is indeed working with Mr. C, then that means he's got friends on the other side like Cooper does. I mean, We knew BOB was with him (though curious where he is now or what even happened to him), but Mr. C seemed pretty isolated from the Lodge to me in a lot of this but it definitely seems like the Arm Doppelganger is working with him.
