Adam linked a performance of the SEP offertory with some harmonized verses. His harmonizations are very pretty and contemporary sounding. Everyone has encouraged him to write them up, which is great. There were once dozens of books in print with such harmonizations that can be easily adapted to a Psalm text. In my own parish, we use these about every second week, just to mix things up a bit. The Hymnal of 1940, as I recall, has many pages of these in the back.
I've just uploaded another book - again, maybe not the best one but it is one - from 1934 called Psalms and Canticles for Worship by J. Todd Ferrier. It contains many dozens of such harmonizations that you can use depending on the Psalm in question. It does take time to set these for choir but the performance does provide rich textures that can be a nice addition to chant.
Nearly any text can be so set, even the weather report, as shown in this famous example.