I came across a very weird example recently. There's this ma

[Vertical Inc]

I came across a very weird example recently. There's this manga called Jinki by Tsunashima Shirou that dates back to 2000 ended with 4 volumes under Square Enix. He continued the series with sequels(or spin-offs, not sure) but switching different publishers each time like Mag Garden, Media Works, and Fujimi Shobo. Not asking about you publishing it for obvious reasons, but in similar situations what negotiations can be done if you found a manga that switched publishers in a similar fashion?

It varies. Sometimes you have to go to each publisher. Sometimes the most recent one may have the rights to the other books. It really depends.
I have no idea about the JINKI situation. But I’d try to avoid situations like these.