Strictly said DX7S is in between Mk I and Mk II by features…
Disk format is not MS-DOS, but Japanese MSX-DOS, so there can be problems with compatibility with other computers - AFAIK from my experience, Yamaha DX7II FD (and also other Yamaha instruments using disks) disks are not easily readable on modern computers.
DX7 Mk I will accept Voice SysEx dump from DX7 II, it will just ignore unknown additional data specific for DX7 II.
Daniel Forro
There are three models of the II -- S, D, and FD. Which one do you have? Because if you've got an FD you've got a very easy way to load sounds -- the OS reads standard MSDOS floppy formats, so patch transfers are super simple. If not then finding the adapter for the cartridge port would be your easiest way to move sounds between the machines.
IIRC, the II reads the sysex format of the original with no problems, so you should be able to do a straightforward patch dump. It doesn't work the other way, from what I remember, but it's been a long time since I did any of this.