I need a word that refers to a society in which there are many distinct tribes. I know a word tribal society, but it may refer to a single tribe not the whole society-I'm not sure though.
Generally the word is:
If you look at the Iroquois native Americans, they are what's called a confederacy.
The Iroquois are a historically powerful northeast Native American confederacy.
...comprising the Mohawk, Onondaga, Oneida, Cayuga, and Seneca. After 1722, they accepted the Tuscarora people from the Southeast into their confederacy, and became known as the "Six Nations".
All the aforementioned native groups are tribes.
The Iroquois have absorbed many other peoples into their tribes as a result of warfare, adoption of captives, and by offering shelter to displaced peoples.
From the Encyclopaedia Britannica:
Five Nations (later Six Nations) better known as the Iroquois Confederacy.
Notice the word "confederation" in the following:
Iroquois Confederacy, also called Iroquois League, Five Nations, or (from 1722) Six Nations, confederation of five (later six) Indian tribes across upper New York Iroquois Confederacy
The word is also used when referring to the Twelve Tribes of Israel from the Bible/Torah. Here they are called a confederation:
In the Bible's version of events, the period from the conquest of Canaan under the leadership of Joshua until the formation of the first Kingdom of Israel, passed with the tribes forming a loose confederation, described in the Book of Judges.
Twelve Tribes of Israel
Another example is the confederacy of the Gallic tribes under Vercingetorix who led the rebellion against Julius Caesar:
Vercingetorix was named the king of the Arverni and general of the confederates.
Generally these two words are used. Probably less commonly "coalition" is used.
Also, if it's of any help, the adjective form is confederative or confederal. So you may say a confederal/confederative tribal society or group. This would mean that they are not separate or generally hostile against each other, because, well, they're confederates.
I suggest 'heterogeneous', e.g. 'the country is a heterogeneous society comprised of three northern tribes'. But there are quite good answers here so which one will work perfectly for you is only depending on the context, I guess.
By the way, I hope what you write about is not of this modern era. As the word 'tribe' connotes 'primative', 'uncivilised', taking 'tribe' instead of 'ethnicity' can be seen as derogatory, you know, esp. for sjw.
plural society (noun)
A society composed of different ethnic groups or cultural traditions, or in the political structure of which ethnic or cultural differences are reflected.
'Britain has been developing into an increasingly plural society'.
I've heard expressions using the word nation. From crystalinks.com:
Apache Nation. Apache is the collective name for several culturally related tribes of Native Americans, aboriginal inhabitants of North America, who speak a Southern Athabaskan language.
The Seminole Nation of Oklahoma is a federally recognized Native American tribe based in the U.S. state of Oklahoma