Final answer:
The opinions that support a majority decision but stress a different legal basis are concurring opinions. These, alongside dissenting opinions, contribute to the Court's legal dialogue and may impact future jurisprudence.
Step-by-step explanation:
Opinions that are offered by one or more Supreme Court justices to support a majority decision, but also to stress a different constitutional or legal basis for the judgment, are known as concurring opinions. While a majority opinion reflects a consensus among a majority of the justices, a justice may write a concurring opinion to highlight an alternative reasoning or legal principle that underpins their agreement with the majority's conclusion. Similarly, justices who disagree with the majority may write dissenting opinions, providing a record of their disagreement and rationale, which can influence future cases and legal thought.