I know this is kind of rediculous, but is there any way to change your civ mid game? Without going through every single attribute, changing it manually? So that it appears, or is essentially a perfect swap? I mean is there an easy way to do it? Or to say, be two civs at the same time? By applying all the changes of another civ to your current one? Easily? 
I can’t think of an easy way to do it. Certainly you could just enable/disable various techs or change attributes to get something close. I might wonder if that’s sufficient for your purposes? Do you really want the entire tech tree and every single bonus to change? Or do you just want to swap out custom units and one or two effects? Because the latter would be quite simple.
That said, you can E: Research Technology and in the options you can select various Civilization names. I’m not exactly sure what that does, however; in testing it didn’t make Persian Paladin’s have Frankish HP, so I’m not sure what it accomplishes.