Something that I picked up from working with great singers was that harmony is there to support the song and the singer.
When I first worked with Alison Moyet in 2002, I had been playing a lot of jazz, so my natural impulse was to fill out harmony with three-, four- or five-note voicings. Alison picked me up on a section where I was adding too much to the voicing, and showed me a dyad (two-noted chord) that was more appropriate. Her exact words were: “Not every chord has to have three notes.”
During the writing of the score for Tales of the City the Musical with Jake Shears, I would often follow a similar impulse to “over-harmonise” things, to which Jake’s usual response was: “Too Jazzy!” I took this onboard, and started writing a lot more using only triads (and sometimes dyads). Surprisingly, this opened up my harmonic language more than I could have expected, because it forced me to think harder about inversions, voicings, modulations and related keys.
As an exercise, I highly recommend limiting your harmonic palette, and seeing where it leads you. For me, it really opens up the potentials of songwriting and composition. Then, when you finally do sneak in a major 7th, a minor 9th or even a 13th with a b5, the effect of it is that much more powerful.