First - the idea of DC16 save, DC15 partial save is already baked into the system in the form of "save for half" effects, but that doesn't sound like what you are looking for - it sounds like you want a graduated system.
I Not exactly seen it as part of D&D, but I've seen systems where the amount that you succeed or fail a roll improves or worsens the effect.
Example: a target number on a d20 to-hit roll is x. You roll y, which beats x by 5. You add 5 to the damage you do on your attack.
For attack spells, the amount your attack succeeds could be added to the base save DC. Exceed that, fully negate the effects. Exceed the base save DC and you take 1/2 damage or something along those lines.
For example:
Level 1 Wizard Joe with Int 16 needs to succeed on a melee touch attack to zap Fred the Fighter with a Shocking Grasp spell. He needs to hit an AC 12. Joe rolls a 17 - success! He beats the roll by 5.
There is no save per the spell, as written. If the spell had a save DC, it'd be 10 + 1 + 3 = 14. Since this is a melee touch attack, you could make this a Fort save. So - the base save DC is 14. The full save DC is 19 (14 + 5).
Joe rolls his 1d6 for damage and comes up with a 4. Fred makes his Fort save and gets a 17. Fred takes 1/2 damage. Had Fred rolled a 19 or higher, he'd take no damage. Had he rolled lower than 14, he'd take full damage.
Another example:
Wizard Joe wants to cast Ray of Enfeeblement on Fred. He again needs to beat an AC 12 and gets a 15 - beating it by 3. This makes his spell save DC 17 (14 + 3). He rolls a 1d6 and gets 5 for the amount of Str he'll weaken Fred by.
Fred isn't having a lot of luck today and gets a 15 on his Fort save.
As written, he'd take no Str damage. Instead, now, he takes 1/2 damage since he beat the base save DC, but not the higher DC caused by Joe's attack roll exceeding the minimum needed to hit.
Another way of doing this would instead be to just stay on the save DC only and figure out by just how much a save is failed and apply that - for rolls that fail by 5 or more being critical failures.
So - let's say instead of rolling a 15, Fred rolled a 12 and failed the saving throw for the Ray of Enfeeblement (but we aren't enhancing Joe's effects by how much he exceeded the needed to-hit roll, so the save DC is just a 14). He failed, but by less than 5 - perhaps this causes 75% of the effect instead of 50% of the effect for making the saving throw. So - his Str penalty is 5, less 1/2 of 1/2. So - instead of 5, he'll take a Str penalty of 4. (since 1/2 of 5 is 2.5, rounded down to 2 and 1/2 of that is 1).
So - Fred failed his save by 3. Perhaps
