Yes, Quivering Palm can be applied multiple times to the same target
Yes, each instance can be activated one by one
To oppose the second part of NautArch's answer (I agree with the first part), I argue that each applied Quivering Palm "is its own thing" (produces its own set of vibrations).
The vibrations are harmless until you use your action to end them.
You can see each set of vibrations as a "different frequency based on the circumstances of the hit". Therefore, each set can be individually ended.
If two different monks apply a Quivering Palm on the same target followed by the first monk activating his Quivering Palm, then the second monk's Quivering Palm is not lost (and can be used later). The logic should be the same when a monk applies two Quivering Palms to the same target.
Even considering the Game features rule...
When two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. [...] Game features include spells, class features, feats, racial traits, monster abilities, and magic items
...You can see one of your stacked Quivering Palms as being the "most potent" (the "strongest vibrations", RP-wise), while the others stay "dormant". Then, once the "most potent" is activated (thus used), you then choose what's the next "most potent" Quivering Palm from your stack to be applied on a later date.
In summary : if you apply two Quivering Palms on the same target, then stop the vibrations for your first Quivering Palm (and get its effects), you can still stop the vibrations for your second Quivering Palm on a later day (and get its effects).