One of the strategies I’ve been using to find new reharmonization in my arranging involves writing outer lines first.
Melody comes first, always. Then, a strong counter-line in the bottom voice. It might be linear, contrapuntal, or functional (fourths and fifths).
With those two written, it’s a question of exhaustively auditioning each melodic note for possibilities, ranging from the most obvious (generally: functional, tonal) to the least obvious (generally: distantly harmonically related, rootless, non-functional, or just plain unexpected).
It works best to decide up front the number of voices. With four-part writing, for example, the lines become clearer once the first two have been chosen. Careful attention must be paid to the strength of the inner lines, though attention need not be focused on such traditional concerns as contrary motion, parallel 5ths, etc.
There was a time when I, like many vocal arrangers, approached arranging by imposing a harmonic scaffolding and then “solving” the specific voicings to fit that scaffolding.
But in the end, much more complex harmony can rest on the backs of strong melodic lines. Working from the outside in like this can often take me to unexpected harmonic places. And because our ears hear horizontally at least as much as they hear vertically, the results are both easier to sing and easier to enjoy from the audience.