On PS2 with multi disk titles, at one point in the story line, the state is saved on the memory card and it's suggested to swap disc or one can reboot the console with the new disc in (I don't recall if I completed Star Ocean 3, but I'm sure that's what happens with Shadow Hearts 2: Covenant and Rogue Galaxy)
Regarding PS4, I think the problem is sharing the memory card between the two images, on PS3 the support was in the firmware and exported on the dashboard, there was also an USB adapter to connect physical PS2 memory cards.