It all depends…
I always start with cymbal mics centered in mono and check phasing (usually at micing stage but I still check during the mix stage in case I missed something)
Rock drums/in your face kinda thing I will HP the cymbals or do a combination highpass lower and shelf after that till the balance of the kit sounds right.
I sometimes “bell in” tom resonances if needed in the cymbal mics.
I boost the highs with pultec or sonnox or my outboard eq for others.
Sometimes I will de-sss to tame them.
Squash the room mic and make it pump. Put a mono to stereo plug on it.
Put a nice reverb on the cymbals to smooth them out then blend to taste considering part to part of the song.
It is all about balance. I’ll set up the mics for the genre and sound I want. Here is a setup for today’s sessions, an isosceles triangle technique with a few close mics for augmentation:
Totally open sounding with softer cymbals.
I guess it all really depends on how and why the overheads were placed first. Then the genre comes into play. If the intention was for the overall kit including the cymbals, I process differently than if I wanted more cymbal focus in the mics. FWIW, I usually place overhead microphones to capture a lot of the kit so when processing, it affects the whole kit sound unless I high pass them.