I have some acetates, aluminum based, probably from the mid to late forties, Spanish, Portuguese and South American.
I have a 5" Victor home recording record in a plastic material, which I cannot date. It has a speech by a Spanish impresario, as the label states, but I cannot get sound from it. Probably I need a very wide stylus.
I have three rarest records, I suppose in Italy they are common... These are flexible celluloid - like records branded Flectar Non Frangar, on vivid orange, and green color, with red paper labels (pressed) that seem to be from the mid twenties. They are 10" operatics, from beautiful puccini arias sung by tenors Voltolini and Bergamaschi. These records are made by La Fonografia Nazionale, Milano.
Another collection is my album of rarities, where I've been joining records from all parts of exotic lands... Serbian, Hawaiian (the very first I had, early in my hobby, which is Kanui&Lula singing Oua Oua and Tomi Tomi

the voice of the singer is peculiarly funny for me, as it sounds as of a man in his fifties or sixties, and songs with a strong raspy voice, that transmits fun and joy) , Japanese, nigerian, Turkish, hindi... A little bunch of exotic records.
I also happened to find a bunch of old Spanish & French G&Ts, 7" sized, recorded in 1902 and the like, in a very old cardboard box, which seems original from the era. These were among the first 400 recorded by Carl Scheuplein in France and in Spain, when he was assigned as chief recorder for the Cie Française du Gramophone.
And of course, the rare crying record from German Beka, in a Spanish Parlophon pressing, paired with the laughing record, also the Beka recording.
Edit. MORE "SPECIAL" chords in my collection...
I also have a box full of Pathé records, mostly Spanish and French issues, operatics and flamenco.
An album of Fonotipia records, mostly operatics.
One blue Indian label Okeh with Old Black Joe.
I also have a Phonycord, several Duriums and HOWs, several Goodsons, and the famous Canadian farting contest records! Several other laughing records, a couple American party records, two albums of fairy tales on records (White Snow, Sleeping beauty and two dozen more stories for children), an album of patriotic songs and marches from the Spanish Civil War (Franco wing), several Standards and Uniteds (Henry Burr and the like)...
But about the rarest records for a Spanish collector, the hmv issue of Ellington Live and live tonight, and Emilio Cáceres Marihuana, still escapes me in 43 years collecting... GRAMÓFONO AE4414, still not a single copy I've ever seen! Another rare (in Spain at least) is Gramófono DB1126, Backhaus laying Schubert Moment Musical in F minor and Impromptu B flat... the only copy I've ever seen I bought it, despite being a british pressing, and having the typical stressed grooves in the low strong piano notes. I say typical because I own a tape copy from my grandpa Spanish Gramófono pressing and it has the same stressed grooves in the same places.
I own three of the Spanish Parlophon recordings by Sam Wooding and his Chocolate Kiddies... rare also. Never have seen another one.
Ah, and an early Carlos Gardel acoustic from 1919, pobre of his very earliest recordings, from Argentine.
I must have more rarities, as my tastes are eclectic and I've collected at least an example of whatever I've seen on 78s in these 43 years!
Another rarity, despite being an enormously popular record in the mid forties, is a Spanish Columbia of the vocal sextet Los Xey singing Buen Menu. They recorded it also for Gramófono, but I've never seen a copy of this. And the Columbia I own is the sole copy I've ever seen. The lyrics of this song are the menu of a restaurant, recited to a hungry client. Three minutes of a list of dishes for every taste! A beautiful Spanish barbershop style singing.