not exactly, following all might' analogy, sharing between old + new main holder is supposed to operate similarly to a an olympic torch, i believe passing is a more accurate term.

https://myheromanga.com/manga/boku-no-hero-academia-chapter-5/

"like when passing the olympic flame, the new torch burns weakly at first but the coming tests and trials will fan it. yes my own flame will slowly wither and die...my duty fulfilled!"

an old + new main holder cannot permanently possess OfA, sharing here is very much a rite of passage. on the contrary, when izuku shared it with bakugo there wasn't any permanent loss on his part, so the rules in play between new main holder + temporary holder are different