My MzABar "Gustate et videte" has a rather simple polyphonic (actually, 3-voice canonic) antiphon plus Mode III chant verses, which are harmonized (but just the chant melody can also be sung).
There is also an English version "O taste and see" with the English verses in harmonized Mode III Anglican chant (which evokes a slimmed down version of the Gregorian Mode III chant).
You do not write for which time of the church year and what you consider "simple polyphony", so it is difficult to make suitable suggestions. As @GerardH already has suggested two of my pieces (one for Maundy Thursday and one for advent), here are some further suggestions for the coming Lent and Easter season:
The Lenten chant Attende Domine with a two part setting of the refrain and stanzas in the original chant tone (editions with Latin or English text).
The Mandatum Antiphone Mandatum novum do vobis with the antiphone set in four parts and the verse chated to the chant melody from the Graduale (editions with Latin, English, or German text).
The Easter chant O filii et filiae with a three part setting of the alleluja refrain and the stanzas in the original chant tone (editions with Latin, English, or German text).
The Easter sequence Victimae paschali laudes with the first verse used as a three part refrain and the rest sung to the 11th century chant (editions with Latin or Esperanto text).
There are many more on my website like Salve festa dies, Haec dies, or Gaudeamus omnes, but these presumably do not fall in the category "simple polyphonic refrain".
Christopher Dalitz has a beautiful but also very doable polyphonic choral setting of the offertory antiphon for Ascension that alternates with chanted psalm verses. And it's available for free on cpdl and he offers it in SSA and SAT settings as well as in English and Latin.
I'm also going to have my choir sing the Vaughan Williams' setting of O Taste and See - which is the text of an ad libitum Communion antiphon - alternating with the chanted psalm verses for the ad libitum antiphon to lengthen it out.
Also, this edition of the Palestrina "Jesu Rex admirabilis," which incorporates a chant hymn as verses. (The text of both polyphony and verses comes from the same 48-verse hymn on the Holy Name of Jesus, composed by St. Bernard of Clairvaux.)
Here are two pieces you can use during Lent: a simple choral refrain for SAB (Grancini's O Bone Jesu) with verses from Psalm 50, and a setting of Attende Domine (melody in the bass) with chant verses.
Besides Jesu rex admirabilis, many chant hymns can work alternating verses of polyphony and chant, though some of these involve more complicated polyphony than the examples above. I've attached two such settings of the Veni Creator adapted from Josquin des Prez and Praetorius, and a setting of the Vexilla Regis for Holy Week. You could also alternate the Stabat Mater by Bragers (found in the Pius X Hymnal) with the familiar chant.
Grancini - O bone Jesu - SABar - with Ps 50 psalm tone - FOR PRINTING.pdf
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Roussel - Attende Domine - chant with SATB refrain.pdf
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Josquin - Veni Creator - SATB (ed Schmitt) - COMPLETE - FOR PRINTING.pdf
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Praetorius - Veni Creator Spiritus - SATB (even verses).pdf
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Feroci - Vexilla regis - SABar with chant - FOR PRINTING.pdf
Ravanello composed a number of works that alternate chant verses with 3 voice polyphony verses. It's not verse-refrain, but a similar idea. You can mine this thread.
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