I suggest following the
wiki instructions for save location. Yes, it is perfectly possible to copy and store the save files elsewhere (as a matter of fact I heartily suggest to do so for backup of your precious game achievements) but the game shall only be able to recognize save files in their original location. Yes, it is possible to open up save spaces and effectively go beyond 14 save slots, but renaming save files can mess with the game's ability to recognize them so I suggest not to do it. Just backup 'old' save files in a different location before you overwrite them with new ones. As a matter of fact, I've been doing this myself and my archive of save files for my main playthrough and preferred version of Steele is about 12+7=19 save files as of now. I keep a "TiTS saves 1" folder with a copy of the old, original 1-12 save slots and a "TiTS saves 2" one with a copy of the new save files I've been overwriting in the 1-7 save slots. If and when I each new major playthrough stages I want to keep as milestone save points, I shall progress to 8, 9, etc. When I reach the 12 save slot again, I shall create a "TiTS saves 3" folder and keep the process.
Usually I keep slot 13 and 14 free for short-term experimentation with playthrough variants, save scumming, or save editing. I used to keep an herm variant of my Steele (the default, most cherished version is hyper-feminine) updated to last playthrough in slot 13, to explore those game events that require Steele to have male genitals, although as of recent I got down to record which traits to save edit to make Steele my preferred version of herm on the fly with TiTSEd, so this might have become superflous.