Justice Stevens also filed a dissenting opinion in which he said there was "no obvious limiting principle" to the majority's analysis.
While also joining the majority, Justice Thomas filed a separate opinion emphasizing the role of school choice on the opportunities available to poor urban children.
He is expected to file a detailed written opinion in coming days.
Justice Stevens had not signed that opinion, filing a dissenting opinion of his own instead.
In the same case, Judge Dyk filed a concurring opinion to similar effect.
Justice Kennedy filed an opinion upholding the regulation on different grounds.
Justice Scalia agreed with the result but filed a separate opinion.
Justice Kennedy filed a brief concurring opinion indicating some unease about his vote.
Justice Clarence Thomas filed a separate opinion agreeing with the result.
John P. Stevens filed a concurring opinion in the result.