It should be noted that the Latin Church accepts the following rites: the Roman Rite, the Gallican Rites (Ambrosian, Mozaribic, Lyonese, Braga), as well as particular rites for religious orders (Carthusian, Cistercian, etc.) 
The Eastern Church accepts: the Antiochene Rites (Maronite, Syrian), the Chaldean Rite, the Armenian Rite, and the Alexandrian Rite (Coptic, Ehtiopian). 
I have always wondered why a church that accepts four very different gospels would insist on uniformity in its liturgy?