Came across this recently in my editing work. I was editing marketing copy, so I just assumed the writer made a mistake. I started to change it to "predominantly," but then stopped and looked it up.
to have ascendancy, authority, or dominating influence (over others); hold sway
to be dominant in amount, number, etc.; prevail; preponderate
In other words, predominately is a lot like predominantly.
I changed it anyway.