What if every character can decide to allocate three of their stats, each to a different save? That would contributte to making every PC unique.
For example, a smart Wizard could be used to employ their superior reasoning and logic to anticipate the perils of the battlefield (improving their Reflex saves), or to make sense of what's going on and maintain clarity (applying to Will saves); it may be a little harder to justify applying Int to Fortitude saves, but I think many players can find a good way to describe how it happens for their character.
While a hulking Barbarian may have trained themselves to rely on their muscles as a source of confidence (+Will), as a way to power through debilitating attacks (+Fortitude), or as an unbreakable layer of defense (+Reflex).
This probably leads to higher saves on average, since every character will pick their best three stats to use, but I find it cool.