For the instance that you want to harmonize a non-harmonic passing tone in a jazz/commercial style 4-way close, here is a tip for you:
Using a process of diatonic harmonization, you can make some smooth and boldly beautiful harmonized lines without interfering with the harmonic make-up, or relying on dissonance.
First, analyze the passage. Does the non-harmonic passing tone occur between two chord tones? It should.
Next, analyze the harmony. Is the melody taking place over an acting I, ii, or V chord?
If so, harmonize the chord tones properly with the passing tone remaining.
To harmonize the passing tone, choose from one of the remaining chords (I, ii, or V) and do so. Meaning, if it was a I chord, harmonize the passing tone with a ii or V. If it was a ii chord, harmonize the passing tone with a I or V chord. And if it was a V chord, harmonize the passing tone with a I (more common) or a ii (rare).
Below are some examples with some rough and basic harmonization:
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