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The only "kit" I know would to be to find a used F350 "crew" cab and put that on your truck. Get the entire cab shell and the rear doors which are unique to crew cabs. Then you can swap over your front doors, dash, etc which will all bolt in. Since a crew cab is longer than a king cab, you'll also need a shorter bed or something.
I understand all this isn't what you have in mind, but the king cab's structural integrity is basically in the area you'd have to cut for doors. Newer trucks are constructed a lot differently in the roof and rear to compensate for that loss of strength. Open both side doors on a new king cab and you can see you're looking at a BIG open hole there. They have quite a bit more hidden structural stuff added to support this big opening. (think crash testing) On crew cabs this is no issue since they have a big post in the middle.
You could do it, but it would be a pain and the results would likely not be anything like what you hoped. Due to the reinforcement needs, I doubt anyone will be producing a kit for this, it's just not practical.
A nice thought though, my son-in-law would love to have an extra door or two on his 89 king cab.
So I'm old and set in my ways and have never really cared about being politically correct. Regular, king, and crew have always been quite understandable to everybody I usually talk to, no matter what brand they drive.
While we're at it, what are we supposed to call a king cab with a third door? Or a king cab with those two extra wannabe doors? Not really being a fan of reading Ford technical literature and sales brochures for entertainment, I truthfully don't know. Hopefully not something embarrassing like "superduper cab".