What you can do is to frequency sweep it with a low Q at a very high amplitude, increase the Q, adjust the frequency, increase the Q, adjust the frequency and keep doing this until you cannot get the Q any higher and until the bell sits at the eye of the noise, then you just cut it out. Once you have spotted the area at the lowest Q, it makes sense to temporarily filter off all other frequencies on the snare so that you can focus on these particular noise frequencies. If you have a lot of monitoring options, it makes sense to use the monitors/cans that best reveil the noise/where the noise is the loudest. Do this at high monitoring volume and remove it just as much as you can until you notice other side effects, then back off a little and leave the cut at that level. If at that level it is still a bit too loud, try to apply a compressor (without re-gain) at the same frequency band to further remove the noise. If after that you still find you want it slightly softer still, try to do a small cut on the same frequency as on the first EQ, after the compressor. If this does not work, add one more setup like this on a different frequency, keep adding cuts until it's gone. Do as little as possible to remove the noise and stay focused on what side effects you notice from the cuts. The snare sound is very important.
It is very important that you use monitors that reveil this noise a lot and that you work at pretty high monitoring volume, so that your cuts don't become too big and too wide. It's like applying reverb, it's so easy to overdo it and hence destroy the mix. Be careful not to let this noise dictate the level at which you set the snare. The vitality of a mix is to a great degree determined by the signal level of the snare. Set it at a vital enough signal level even if it becomes hard/harsh and even if it makes the mix clip, then cut out the noise/harshness. When in doubt, stay loud. The vitality factor is always a priority above everything else. If you lose the signal it doesn't matter how clean it is, it is still going to suck the life out of the mix. Set the vitality of each sound source where it needs to be, then deal with the noise/harshness through subtractive EQing, frequency band compression and volume/EQ/compressor automation at loud monitoring volume and as little as possible. It also helps to mute the bass guitar when you balance the snare, so that you can make the snare cut through much enough first of all. Then when you add the bass guitar you can set it at a vital level, initially having the kick and snare muted. Then once you know the bass is overall at a vital level you unmute the kick and snare. You then re-mute, un-mute and pay attention to the punch. Then you side chain the punch frequencies to ensure the kick and snare cuts through the bass guitar and do subtractive EQing until you are satisfied with the sound of all three. This works because in the result you have much enough signal assigned to all three, hence the mix stays vital rather than scooped and lifeless. Sometimes there might be some residues left, but hey, that's what mastering is for.
When I bring my mixes to mastering, I do so at a point when everything is perfect except I can notice some minor residues here and there that makes the overall sound a little unpolished. In mastering I make it sound polished and commercially competitive in the particular genre. That requires a certain overall balance quality in terms of the MID and SIDE components.