When justices agree with the ruling of a court majority but not all of its reasoning, they may often write a (n)

A concurrence.

Explanation:

A concurrence, or a concurring opinion is a decision made by a judge or several judges within a given court. In situation, when a judge partly agrees with the opinion of the court's majority, but has an additional angle to present. In this way, a judge provides reasoning for their decision. When several concurring opinions are present, an opinion shared by the greatest number of judges become a plurality opinion.