[ Wiktionary for *metipsimus :] Etymology
[0.] From -met (emphatic suffix) + ipse (“himself”) + -issimus (superlative suffix).
Adjective
*metipsimus (feminine *metipsima, neuter *metipsimum); first/second declension
What semantic notions underlie 0 and 1 above? How did 0 semantically shift to 1? I.e., how does compounding 'himself' with 1 emphatic and 1 superlative suffix generate the meaning of 'same'?
The key to the meaning is ipse; all the rest is just intensifiers glommed onto that.
In Classical Latin, ipse meant "self"—not as a reflexive, but as an intensive:
Barack Obaman ipsum apud tabernam vīdī!
I saw Barack Obama himself at the store!
This eventually took on a meaning of "same":
Barack Obaman vīdistī? Praesidentem emeritum?
You saw Barack Obama? The former President?
Ita, Obaman ipsum!
Yes, the very same Obama!
The implication, of course, being "the very same person that you're talking about".
But in Vulgar Latin, ipse weakened over time. The Latin demonstratives were worn away until their force was lost and they became nothing but articles; ipse then lost its intensity and became a normal demonstrative. We see it now in forms like Spanish ése, "that".
So when speakers wanted the actual "same" meaning, they had to bring back the intensity. Sometimes they added superlative endings, as in Petronius's ipsimus; other times they added the intensive -met suffix onto the beginning, from rebracketing tēmet ipse "you, you yourself" as *tē metipse. Eventually they had to combine both to get the proper intensity back, ending up with *metipsimus.
This is the form that survived into Romance, giving us words like Italian medesimo and French même < meïsme, which can either mean "same" or be a raw intensifier ("very" or "even").
Like Draconis stated, it's the weakening of the original word that caused it to be a demonstrative to fill the void that ille and iste left. It's similar to what happened in our language, "the" was originally a demonstrative as well in Old English, but weakened to merely a definite article totally in Middle English.
I believe the addition of the meaning "same" was the result of īdem falling out of favor in colloquial speech, so metipsimus filled that void as well. In Spanish, "mismo", it's cognate, can be used to mean both.
The Vulgar Latin metipsimus, as a contraction of older metipsissimus, a superlative of metipse, comes from a reanalysis of egomet ipse "me myself" as ego metipse. In Latin, -met was attached to pronouns, but in Vulgar Latin it was reanalyzed as part of ipse instead.
