There are 23 branches of the Catholic Church. The Latin branch is only one. The Maronite is another, but there are 21 more Eastern branches, including many from the Byzantine tradition. You also do not need to change rites officially. You can attend any church as long as you like, and even become a member of their parish, without officially changing rites.
**The 23 branches of the Catholic Church are (the dates listed refer to the year of reunification with Rome):
Western tradition**
- The Latin Catholic Church
**
Alexandrian Tradition**
- Coptic Catholic Church (patriarchate): Egypt (1741)
- Ethiopian Catholic Church (metropolia): Ethiopia, Eritrea (1846)
Antiochian (Antiochene or West-Syrian) tradition
4) Maronite Church (patriarchate): Lebanon, Cyprus, Jordan, Israel, Palestine, Egypt, Syria, Argentina, Brazil, United States, Australia, Canada, Mexico (union re-affirmed 1182)
5) Syriac Catholic Church (patriarchate): Lebanon, Iraq, Jordan, Kuwait, Palestine, Egypt, Sudan, Syria, Turkey, United States and Canada, Venezuela (1781)
6) Syro-Malankara Catholic Church (major archiepiscopate): India, United States (1930)
**
Armenian tradition**
7) Armenian Catholic Church (patriarchate): Lebanon, Iran, Iraq, Egypt, Syria, Turkey, Jordan, Palestine, Ukraine, France, Greece, Latin America, Argentina, Romania, United States, Canada, Eastern Europe (1742)
**
Chaldean or East Syrian tradition**
8) Chaldean Catholic Church (patriarchate): Iraq, Iran, Lebanon, Egypt, Syria, Turkey, United States (1692)
9) Syro-Malabar Church (major archiepiscopate): India, United States (at latest, 1599)
Byzantine (Constantinopolitan) tradition
10) Albanian Byzantine Catholic Church (apostolic administration): Albania (1628)
11) Belarusian Greek Catholic Church (no established hierarchy at present): Belarus (1596)
12) Bulgarian Greek Catholic Church (apostolic exarchate): Bulgaria (1861)
13) Byzantine Church of the Eparchy of Križevci (an eparchy and an apostolic exarchate): Croatia, Serbia and Montenegro (1611)
14) Greek Byzantine Catholic Church (two apostolic exarchates): Greece, Turkey (1829)
15) Hungarian Greek Catholic Church (an eparchy and an apostolic exarchate): Hungary (1646)
16) Italo-Albanian Catholic Church (two eparchies and a territorial abbacy): Italy (Never separated)
17) Macedonian Greek Catholic Church (an apostolic exarchate): Republic of Macedonia (1918)
18) Melkite Greek Catholic Church (patriarchate): Syria, Lebanon, Jordan, Israel, Jerusalem, Brazil, United States, Canada, Mexico, Iraq, Egypt and Sudan, Kuwait, Australia, Venezuela, Argentina (1726)
19) Romanian Church United with Rome, Greek-Catholic (major archiepiscopate): Romania, United States (1697)
20) Russian Byzantine Catholic Church: (two apostolic exarchates, at present with no published hierarchs): Russia, China (1905); currently about 20 parishes and communities scattered around the world, including five in Russia itself, answering to bishops of other jurisdictions
21) Ruthenian Catholic Church (a sui juris metropolia, an eparchy, and an apostolic exarchate): United States, Ukraine, Czech Republic (1646)
22) Slovak Greek Catholic Church (metropolia): Slovak Republic, Canada (1646)
23) Ukrainian Greek Catholic Church (major archiepiscopate): Ukraine, Poland, United States, Canada, Great Britain, Australia, Germany and Scandinavia, France, Brazil, Argentina (1595)
Any Catholic is free to attend the services, liturgies, and sacraments of ANY other branch of Catholicism at any time.
The problem is that the 22 Eastern branches of the Catholic Church
together make up only a tiny fraction of the total number of Catholics. That said, EWTN does broadcast the Divine Liturgy from time to time.