I’ve read some stories of someone transmuting Ubuntu into Debian or something like that. It requires lots of knowledge of both systems, plenty of time, and infinite patience. The two distributions should be somewhat closely related in order to make this gargantuan project even remotely feasible. If you’re jumping from Arch to Gentoo, you might as well just do LFS while you’re at it.

Technically, if you had tons of time and a solid understanding of Linux inside and out, you might be able to pull it off, but it’s not worth the hassle at all.

This is what I thought. Preferably “from the outside” i.e. while the system isn’t running. But all you “saved” in the end is the filesystem the original OS was installed on, and possibly personal data (which probably is the reason OP is even asking).