Any tips and tricks for working with harmonics?

As an intermediate-level composer and songwriter, I'm still at the stage where harmonics seem magical and weird. I love doing narrow EQ sweeps and marvelling at the presence of all these ghost tones in what sounds like a single musical note. I'm only just starting to recognize the different ways that harmonics can accentuate or mess up a mix, so I'm curious to hear any tips or anecdotes you might have.

For example, how do you use particular exciters for particular effects (e.g. tube vs tape)? Do you often encounter recurring "problem" harmonics with certain instruments, or conversely, harmonics that just love to be boosted? Any interesting realizations about how harmonics are distributed across the spectrum?

Basically I just love the weird guys and I would love to hear your thoughts on them.