Welcome to CAF, @haleyhenry.
What you describe sounds very similar to Canons Regular:
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Canons Regular of Saint Augustine of the Congregation of Windesheim (22 members)
Canons Regular of the Congregation of Saint Victor (68 members)
Canons Regular of the Congregation of Brothers of Community Life (26 members)
Canons Regular of the Congregation of the Most Holy Saviour of the Lateran (198 members)
Canons Regular of the Hospitaller Congregation of the Great Saint Bernard (40 members)
Canons Regular of the Congregation of the Immaculate Conception (48 members)
Canons Regular of the Lateran Congregation of Austria (150 members)
Canons Regular of the Mother of God (36 members)
Canons Regular of the Order of the Holy Cross (Crosiers) (347 members)
Confederation of Canons Regular of Saint Augustine (584 members)
Knights of the Cross with the Red Star (20 members)
Order of Canons Regular of the Holy Cross (140 members)
Order of the Canons Regular of Prémontré (Norbertines, Premonstratensians) (1184 members)
Order of the Teutonic Knights of Saint Mary’s Hospital in Jerusalem (Teutonic Order) (87 members)
Swiss Congregation of Canons Regular of Saint Maurice of Agaune (32 members)
Canons Regular of Saint John Cantius (5 churches)