"A number of reports indicate that the justices, while agreed that segregation was wrong, were divided over whether the Court had the power to overrule Plessy. They therefore set the cases down for reargument in 1953, specifically asking both sides to address particular issues. Then Chief Justice Vinson, who reportedly opposed reversing Plessy, unexpectedly died a few weeks before the reargument, and the new chief justice, Earl Warren, skillfully steered the Court to its unanimous and historic ruling on May 17, 1954." (http://usinfo.state.gov/usa/infousa/facts/democrac/36.htm
As it was a unanimous ruling, there aren't any dissenting opinions to discuss. My educated guess is that a unanimous ruling precludes the possibility that there are concurring opinions.
For the sake of the assignment, however, we're only to use what Duq provided.
What I would REALLY like to know is the proper format for the memorandum that we're to have mailed by the end of the month. I have my answer, but I need to fit it into a memo format that is appropriate for a law clerk to send to a justice.