My halakha teacher (who prefers not to be cited by name) has dug up a somewhat arcane form of kinyan in the sources, called “kinyan hithaivut,” or “acquisition by self-obligation.”
It’s a form of kinyan sudar (meaning, the acquisition has to happen over an object) in which a person can self-obligate himself to do something. (See Baba Metzia 67b, 108a, 47a, and Encyclopedia Talmudit on Hithaivut.)
He notes that since “mikudesh” (set apart) has a very specific meaning in this context, and since one technically can’t make a man mikudesh, one shouldn’t say, “harei, atah mikudesh li” (aka the masculine formula of the traditional kiddushin formula.) Rather, the bride handing the groom the object (ring, most likely) over which he would self-obligate himself would be better off saying something like, “Harei atah mihuyav b’kinyan sudar zeh sh’lo likayem yachasim im nashot b’olam hutz mimeni” (Behold, you are obligated with this kinyan sudar not to engage in sexual relations with women other than myself.)
It’s not clear if the groom, through this kinyan, is being acquired, or not. One could argue both ways, frankly. Certainly, the groom is obligating himself to monogamy through his acquisition of a ring just as he obligates the bride to monogamy through her acquisition of a ring. It’s not a perfect parallel, but it’s pretty close.
There is some question about whether a person can use kinyan hithaivut for commitments not to do something in the future, which means that it is safek derabbanan (whereas kiddushin of a woman is vedai d’Oraita,) but still could be considered binding.
ADVANTAGES: Both bride and groom get acquired, in a way, obligations of bride and groom are relatively parallel, ring exchange has halakhic meaning on both sides, kosher kiddushin.
DISADVANATGES: The status (safek derabbanan vs. vedai d’Oraita) of the two acts are not equal, like the Linzer model, the groom still acquires the bride and the bride does not acquire the groom, but rather the groom acquires other obligations.