this might be worth considering:

http://www.ccwatershed.org/motecta/

I've been nibbling at an Italian manuscript from 1755 which is available on Internet culturale (http://www.internetculturale.it/opencms/opencms/it/main/esplora/arti/musica/) It's entirely for 3 men's voices (without continuo), and consists of works by Francesco Feroci, his student Bonaventura Matucci, and the mysterious A.M.D. The works are free motets, hymns, introits and graduals (few offertories or communions, which are what I'm looking for), masses, etc. I have 2 of the Feroci settings up on cpdl. He was the chief organist at florence Cathedral 1719-1750 (succeeding his teacher G.M. Casini, succeeded by Matucci). The works are 2 parts in tenor clef and one in bass. The 2 tenor lines are generally the same range (up to f', so not so high), but the 2nd part definitely has a lower tessitura. They're attractive, well-made works in the Baroque prima prattica style. I'll be editing more of these as I find time. If you do a search for all music manuscripts, these pop up at the pages in the 350 range and again at the 490s, or do an author search.

There are collections of music for 3 equal voices out there, but they are often very difficult to find.

CPDL currently has the following 66 works classified as Sacred music for TTB voices:

A solis ortus cardine a 3 (Gilles Binchois)
Adoramus te (Oreste Ravanello)
Adoramus te, Christe (Giovanni Battista Martini)
Adoramus te, Christe a 3 (Orlando di Lasso)
Amor potest - Ad amorem (Anonymous)
An Wasserflüssen Babylon (Michael Praetorius)
Angelus ad pastores ait (Claudio Monteverdi)
Anima mea liquefacta est (Guillaume Dufay)
Ave Maria (Claudio Monteverdi)
Ave verum corpus (Christoph Dalitz)
Ay, Santa Maria (Anonymous)
Beata viscera - Corsican chant (Anonymous)
Christus factus est a 3 (Giovanni Matteo Asola)
Danket dem Herren (Andreas Rauch)
Deutsche Messe (Johann Michael Haydn)
Dextera Domini (Francesco Feroci)
Dixi confitebor (Orlando di Lasso)
Ecce sacerdos magnus (Francesco Feroci)
Eripe me a 3 (Orlando di Lasso)
Es ist das Heil (Michael Praetorius)
Gabriel angelus (Mathias)
Gloria (Guillaume Dufay)
Gloria laus (Guilio Bas)
Gustate et videte (Giovanni Matteo Asola)
Gustate et videte (Giovanni Paolo Cima)
Hodie apparuit in Israel (Orlando di Lasso)
Hoquetus David (Guillaume de Machaut)
How can I keep from singing? (Patrick O'Shea)
Huic ut - Huic ut (Anonymous)
Huron Carol - Jesous Ahatonhia (Traditional)
Ich bin die Auferstehung, SWV 324 (Heinrich Schütz)
Ihr unsre neuen Leiter, K 484 (Wolfgang Amadeus Mozart)
Im Anfang war das Wort (Markus Pfandler)
In monte Oliveti (Giovanni Battista Martini)
In quacumque die (Orlando di Lasso)
Introitus: Requiem aeternam (from 'Messa da Requiem') (Lorenzo Perosi)
Little Lamb (George Whitefield Chadwick)
Longe mi Jesu (Claudio Monteverdi)
Magnificat (Alessandro Grandi)
Magnificat Sexti Toni a 3 (Christoph Dalitz)
Mass for Three Voices (Antonio Lotti)
Messe brève (Charles Gounod)
Messe brève en Sol (Théodore Dubois)
Miserere - Corsican chant (Anonymous)
Missa I in A Minor (Antonio Lotti)
Missa in F&C (Karl Kempter)
Missa pro defunctis (Giovanni Matteo Asola)
Missa tribus vocibus (Christoph Dalitz)
Nihil tibi (Francesco Soriano)
O amantissime Iesu (Francesco della Porta)
O felix anima (Giacomo Carissimi)
O quam tu pulchra es a 3 (Alessandro Grandi)
O sacramentum pietatis H 260 (Marc-Antoine Charpentier)
Panis angelicus (Lorenzo Donati)
Plange quasi virgo (Oreste Ravanello)
Pues que no puedo olvidarte (Ginés de Morata)
Salve festa dies (Christoph Dalitz)
Salve Regina a 3 (Marc-Antoine Charpentier)
Sophia Nasci Fertur - O Quam Pulchra Racio - Magi Videntes Stellam (Anonymous)
Tantum ergo (Antonio Bergamo)
Tantum ergo (Giuseppe Tartini)
Tristis est anima mea (Giovanni Battista Martini)
Veni Emanuel (anonymus) (Christoph Dalitz)
Verbum caro (Orlando di Lasso)
Volsvi, Persidstii tsarie (Znamenny chant)
Voskresni Bozhe (Pyotr Ivanovich Turchaninov)

CMAA member Matt Williams just composed a new Mass setting for his three-part boys choir. Perhaps he would be willing to share it with you.

Do you have any digital copies that can be (legally) shared?

It would be difficult (perhaps, even, presumptuous,) to better CHG's lists, so I shant even try. One should, though, be aware of the superb set of twelve Cantiones Duarum Vocum, by Orlando Lassus, which contains rather short (two-page) motets for two equal voices. The texts vary from prophecy, proverbs, psalms, plus, some of them extol the virtuous life and one (Sicut rosa) is an exquisite Marian motet. My edition is Mercury, which I got decades ago. Someone should still have them in print. They are priceless as smaller repertory for weddings and such, or for 'fillers' in a liturgy with multiple repertorial needs. Several are even appropriate for funerary or requiem needs, the spiritual life, and stewardship.

Being for two equal voices, they should be sung by 2 trebles, or 2 altos, tenors, or basses. They may be sung at a pitch convenient for the performers.

There is, of course, numerous other literature for 2 or 3 vv. by composers such as Carissimi, Monteverdi, and others. Schutz has a superb collection of solo and continuo Geistliche Konzerte with may be had from Peters and others. These are psalm-based and are valuable as anthems to grace that special spot for which nothing else could do.

Oh! And don't be ashamed to do rounds and canons once in a while. Some of them are quite challenging, and are sophisticated enough that they could very well be fit at some point to grace the liturgy. There is a list of hymns that work in canon in the back of The Hymnal 1982 - and there are others.

If you are not afraid of highly distilled artistry and craftsmanship, there is very much in the late mediaeval or early renaissance era which requires but two or three voices: Dunstaple, des Pres, Binchois, et al. Too, Oxford has several anthologies of SSA or TTB, or other combinations of three and two voices

If you have any compositional or harmonising skill you could arrange some hymns that you like as 3 voiced anthems.

FWIW I've just prepared "Peccantum Me" by Crecquillon for our choir for this Sunday (pdf attached). It's SAB, but can be worked around.
Peccantum Me mp3 here

hi Ryand,
do you still need a new mass setting in english?

A whole book of 3 voice motets:

http://www.chantcafe.com/2014/03/secunda-anthologia-vocalis-3-voice.html