I finsihed this game and save a lot and did not experience any limit to the number of slots it could save to. An arrow appears so you can go to previous 'pages' of saves, I therefore think it likely unlimited.
If the autosave feature is used such as near the end of the game where the game has two endings possible, to allow you to try each, the autosave will be at the page one of saves, something to note if you cannot find it near your recent saves.
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vic