Since this is the 531 forum, I'll answer with that system in mind.
No, don't stagger deloads. Either deload every fourth or seventh week, depending how you run it.
However, you can absolutely stagger TM resets, because not all your lifts will progress at the same rate. So, reset each TM as required.
If you aren't running 531, I see no reason not to stagger deloads if you want to, although I would question the wisdom of doing it. If you're dominating your squats but your other lifts feel slow and heavy, chances are before long your squat will feel that way too because you're getting worn out. Taking a deload across all your lifts won't stop you dominating your squats, and will also let you recover a bit more so your other lifts start feeling good again.