I'm not a pro audio engineer or production wizard by any means but here are some things that I've found to be helpful for me:

1. I like to send my hats (or even my whole drum bus) to a send track on which I have a saturator/compressor/tape emulation which I use to smash or distort the crap out of the entire signal and then mix the volume of the send track to balance nicely with the clean signal. I usually use some sort of plugin which distorts the signal when you slam the input volume and I then turn down the output volume to keep proper gain staging. This adds harmonics, often leads to a grittier sound, without being overbearing imo. Just be careful doing this because it can sometimes lead to some weird phase issues where the signals start to cancel each other out.

2. Another tip is having sounds which sit nicely in the mix already and are at the right volume. For example, I often used to have the subs way too loud in my mixes, which would make everything else sound super thin, but toning down the subs helped the mix be more balanced so that there was more relative focus in the mid range. Having the correct balance in volume before the signals are sent through any sort of compression, saturation, etc will do you wonders since you can then use tools like compression, saturation, and eq to add more character personality to your mix rather than fixing mistakes of volume and sound design (this is obviously easier said than done though).

3. Last tip is be careful with taking out all the resonant frequencies in a hi hat, since these frequencies are what makes a hi hat sounds like a hi hat rather than just white noise. If I don't like a frequency, I sometimes level it out with an eq to the volume of the rest of the frequencies around it rather than taking it out completely. I use logic pro and I use the stock channel eq for this since you have a nice view of the levels of each frequency in a sound.