Parasite Eve if I remember correctly it gave problems to change disc. For this and other games that do not allow saving before changing disc, like Heart of Darkness, I use these patches to join the CDs in one and save some space in the process:
https://www.ngemu.com/threads/disc-combining-kits.118402/page-10
On the first page the compatible titles and on page 10 post 197 you have a public link working with these patches and you do not need to register:
In this forum he summarizes the previous content:
http://www.ps2-home.com/forum/viewtopic.php?t=104
The patch for Chrono Cross has a virus and is not working. To continue playing the second CD you need the patch that Psychospacefish published a few years ago and that what it does is deactivate the request of CD 1 to insert the second disc when you first access Fate of Destiny, allowing the next area to pass without interruption and being able to save within the game on the world map as normal. Then you load CD 2 and you can safely continue your adventure by loading the game from the game menu.
To restart a New Game + there will be no problems because CD 1 reads the saved and finished game from CD 2 independently (save the game in memory card 2). So this way you can play the full game normally.
The Psychospacefish patch is no longer easy to find, here you can see it in its original forum::
https://web.archive.org/web/20100311024220/http://www.maxconsole.net/showthread.php?64516-My-Multi-Disc-switch-patches-(Parasite-Eve-Chrono-Cross-Metal -Gear-Solid% 29
The only place where I have seen the active file to download (ccfix) is in this forum, which requires registration:
http://forum.gamevn.com/threads/vai-ban-fix-de-khac-phuc-loi-thay-dia-cua-game-psx.341353/
Anyway I provide it as an attachment to the post (rename the bin as the author indicates and click on patch.bat).