What does the Supreme Court do?

Generally, the Supreme Court deals with larger issues rather than a two-party conflict. So, they might accept to do a court ruling on a matter between two smaller parties if there is a larger issue at hand. For example, there was the case of 1954 case Brown v. Board of Education of Topeka. Although this was not between large corporations they dealt with this because it involved a large social issue at the time. They ruled that racial segregation in public places is unconstitutional. They then can settle the dispute between the parties, but they need to rely on the other branches of government to work on fixing the issue nationally. You can see this in this specific example by how there was no implementation for fixing the racial segregation for years to come.