When a Supreme Court justice agrees with the decision reached by the court in a case, but not with the reasons why the court made that decision, he or she may choose to write a

The Supreme Court decides to hear a case based on at least four of the nine Justices of the Supreme Court agreeing to grant the Petition for Certiorari. If four Justices agree to grant the petition, the Supreme Court will consider the case ... A petition for Writ Certiorari is a request that the court hear your case.