I'm looking for an isekai manga where the main character gets summoned from one world to the next rapidly, acquiring more power each time. He gets summoned as a hero, a demon lord, a vampire, and one time some magic eye researcher tries to take his eyes. There was a summoning room where a goddess gave him a power each time. Each time he was summoned it would be mere minutes before he was summoned to another world again leaving no time to do anything.
I Was Summoned to a Parallel Fantasy World for Too Many Times (original title Meccha Shoukan Sareta Ken or めっちゃ召喚された件 ～世界法則無視のチート権化～)
A boy’s whole class gets summoned to another world, except he’s the only who one was transferred to a different one. Just when he gets used to his new life, he gets summoned to another world again, and again.
I poked around and found a scan of it and indeed, one of his early misadventures involves the magic eye researcher going after his eyes.
Found by searching for
isekai manga summoned repeatedly, which brought me to this listing with Google having shown an excerpt mentioning the promising title of I Was Summoned to a Parallel Fantasy World for Too Many Times which I then followed up on.