Firstly, this is merely a thought exercise... not a practicality/cost effective exercise... Given the will to ignore/abandon any warranty claim... and the need to exercise my engineering tendencies... The thought has crossed my mind recently to see if I can't figure out how to fabricobble up a trailer equipped with a REX from an i3s and figure out how to incorporate that in some way into a towable range extender aftermarket option for the Mini SE... I think it should be possible given the REX option in the i3(s) family... Practical? probably not... warranty complaint? certainly not.
Maybe this hitch option (see installation guide) is along the lines you're thinking of? I was looking at the similar bike rack modification. Not sure if either of these would work on the SE, the backend/undercarriage are quite different. And I sure wouldn't want to drill into the batteries!
After watching the Plant Oxford assembly videos many times, I know that the rear end of the battery extends only as far back as the front of the rear brake rotors. However, it would be a shame to have to modify the SE's unique rear end that doesn't include cut-outs for the exhaust pipes (they included a fake hood scoop, why not fake exhaust pipes, too?). Perhaps you could purchase the lower-rear body piece made for a MINI Cooper S drag the hitch out from its mounting points there. Hmmm, do the center-exiting exhaust pipes on the MINI Cooper S preclude a trailer hitch on that car? I doubt the wiring of an i3's REX would be as simple as mounting the trailer hitch. Just the routing of the wires would be problematic even if you found out where to attach them. For my thought experiment--finding out how far my (impending) SE will go on a charge--I've planned to stick my little Honda inverter-equipped generator in the boot and bring a book to read. It should only take about an hour to get enough charge to limp home, depending on from where the limping begins. Perhaps to minimize the limping distance I'll drive laps around my neighborhood when the dire warnings start lighting up the instrument panel.
oh, for sure, I actually have no intention of doing this... think of it like the lottery game where you playfully think about options and possibilities that will never actually happen but would be fun to see. Realistically if you are thinking of doing this as well, you chose the wrong vehicle... just charge the damn thing and drive it like it was meant to be.
It does make one think about roadside assistance, like AAA. They'll bring someone a canister of fuel, but do they have charging trucks that will come out to give a DC fast charge to get you on your way? It seems AAA is trying it in limited markets.
I did see an 'emergency charging pack' thingy for teslas, etc... but I think it would be simpler to just dispatch a flatbed and tow it rather than haul around batteries or an APU.