There is possible middle ground for those that like save-or-suck and those that prefer making a saving throw every round.
This is but one such example.
 
(a) Spell is cast, if the victim succeeds proceed to condition 2. The round thereafter you shake off the effect completely.
(b) Spell is cast, if the victim fails proceed to condition 1. Thereafter make a saving throw every round and once you succeed proceed to condition 2 as per (a) above or in the case of Petrification follow the path based on the success or failure of the saving throws.
Hold Person
1. Restrained
2. Staggered (stiffened) - half movement, no bonus action
 
Sleep (I know it works on hit points but in the instance where it worked differently and for the sake of the example)
1. Unconscious (asleep)
2. Staggered (drowsy) - half movement, no bonus action
 
Petrification 
1. Restrained - Paralysed - Petrified
2. Staggered (stiffened) - half movement, no bonus action
		
		
	 
Sounds like the condition track, no?
If so, perhaps we could even make it have either 3 or 5 steps as desired for any particular effect, like so:
Hold Person (concentration; see text)
-2: Paralyzed for one minute, concentration no longer required
-1: Stunned and Restrained
0: Dazed (can only take 
one of: action, bonus action, or move) and Restrained
+1: Dazed and Slowed
+2: Slowed until end of next turn, spell ends
This way, a spell isn't wasted if the target immediately succeeds on their first saving throw. They could fail the second, and still have 
some effect no matter what. You're taking a minor gamble; if the creature has a 50/50 chance to make its save, then it's liable to keep vacillating between -1 (one net failure) and +1 (one net success), but if it passes that first save, there's a 50% chance that it only suffered two turns of debility.
With this, it's a tactical choice, and you can't easily dismiss the value by saying "oh well it fails half the time so don't bother". It's too complex to permit a simple evaluation--tactical analysis is 
required in order to know if it's worth using or not.
And, in contrast to what I said to Lanefan above, 
this is something that absolutely should work both ways. Players absolutely 
should be subject to effects of this kind just like they subject their opponents to such. Because now they've got choices, they've got responses they can make. Especially if we bring back what 4e did, making support-focused characters good at helping others break out of these effects.
It'd also give a potential mechanical niche for the Controller role, which 4e lacked: they could have a feature which lets them partially negate successful enemy saves, meaning the opponent stays where they are on the condition track, but only a very limited number of times per encounter (presumably, two, just as Leaders got two heals per encounter). That's a powerful tool, but you want to use it judiciously. Just blowing your two "that success didn't happen" effects ASAP might help early on, but the same can be said of blowing through your Leader heals right way rather than saving them for a rainy round.
Pure spitballing, of course. Would need much design effort to ensure that it makes sense. But the core idea seems sound to me, and wouldn't require any major effort on anyone's part beyond what you were already doing for the condition track.