More formal:
* Primarily
* Chiefly
* Mainly
* Mostly
* For the most part
* In the main
* By and large
More informal:
* Mostly
* Mainly
* For the most part
* Generally
* Typically
* Usually
* Often
More specific:
* Heavily (if something is dominant in a very large amount)
* Overwhelmingly (if something is dominant in a very large and clear way)
* Significantly (if something is dominant in a notable way)
The best alternative will depend on the specific context of your writing.