There are two ways that you can go at this.
1. You can do a mtDNA test. Mitochondrial DNA is passed down from mother to child, so this type of testing is useful for determining your maternal pedigree (mother's mother's mother) as well as discovering your "deep ancestry" (where your ancestors lived thousands of years ago). Unfortunately, it is often quite hard to follow maternal ancestry back more than a few generations, because women change their names upon marriage or remarriage and paperwork is very confusing. Genealogists are still learning how exactly to fit mtDNA tests into their research.To order an mtDNA test, go here
2. I would recommend ordering a Y-DNA (Surname) test. This is the same test that you've already done, but, to get information on a different branch of your family, you'd need to sponsor having a male relative in that branch get tested for you. For instance, if you wanted to learn about your mother's paternal line, you could get a maternal uncle tested.To order a Y-DNA test, go here