Pretty simple question: when a justice writes a majority or dissenting opinion in which he or she is joined by other justices, do the joining justices offer their own language or do they simply read the opinion and decide whether or not to enter their votes as concurring?
The accurate answer ia “Yes”. 
The final opinion is the product of the justice signing it, in the sense that he has edited, revised, and signed off on the entire content of every bit of it. Portions of varying size will have been drafted by his law clerks to his specification. (“Folks, we’re writing Zotti v Adams. Preston, you take the findings of fact. Margaret, work up a draft of the Sixth Amendment violation. Be sure to cite Alexander and Wright, and distinguish off the contrary holding in Burgess. Pete, work up an outline of the due process implications, and bring it to me to discuss. I’ll rough out the opening and closing so you see what our theme will be.”) Other justices may suggest language or reasoning, and sometimes will insist on points important to them being addressed as the price for their concurrence. Some justices will write virtually the entire opinion from scratch, but the more common practice is the team approach noted above, with the justice functioning as redactor of the final product into something that is ‘his’, that he’s pleased to put his name on.
Justices may ‘join’ an opinion at any time from the assignment after the initial vote until, essentially, the point it’s announced in open court. But normally they will join after reading the draft opinion, sometimes seeking changes before being willing to do so.
If you’re asking whether they collaborate on writing opinions, I think it’s pretty clear that they do. We have the papers of some deceased justices which include memos back and forth discussing the language of particular decisions.
The justices have more options than simply voting up or down on a case. They might agree with the majority but for a different reason, and justices might disagree for different reasons. Justices can write their own opinion, or simply attach their name to part of someone else’s opinion.
A great illustration of how this works can be seen in what of the Court’s most famous cases, Roe v Wade. Justice Blackmun wrote the majority opinion and six justices joined with him (ie, attached their name to what he wrote). Justices Burger, Douglas, and Stewart also wrote concurring opinions, in which they offered more explanation. Justice White wrote a dissenting opinion, which Justice Rehnquist joined, and the Rehnquist wrote his own dissenting opinion with additional comments.
So a 7-2 vote in that case, with six different opinions.
A little of both. Usually one justice (or his clerks) drafts the opinion and circulates it among the other justices, who will suggest revisions and return it for rewriting before approving it as the majority opinion. If a justice concurs but wants to write separately to include something that didn’t make it into the final draft, they write a concurring opinion.
They can do either, it depends on the case. Sometimes a justice will just sign his name to an opinion written by another. Sometimes he’ll sign his name to an opinion, but add a separate short concurring opinion outlining a few issues he wants to bring up that weren’t in the main opinion. Sometimes he’ll write an entirely separate concurring (or dissenting) opinion.
Thanks, guys. I think my question is pretty well-answered.
As a fascinating example of how this process can work, you might want to take a quick look at the discussion of the Dred Scott case in this unfortunately contentious thread. The opinions can be found here.
Often the justices will agree on certain language and all sign on to make a stronger political statement. In Brown v. Board of Education of Topeka the justices negotiated internally to produce one unanimous statement so that nobody could seize upon any deviations to find a loophole to crawl through.
The utter reverse of that was Dred Scott. There were six separate concurring opinions, some of which disagreed with Taney’s reasoning about everything except the final conclusion, and two separate dissenting opinions.
Similarly, each of the dissenters filed opinions in Bush v Gore.
The Court is a political body. That doesn’t mean that all or even most cases are decided by political concerns. The Court also will often go out of its way to avoid a purely political case. They are sometimes unavoidable. And when they are, you can see that the Court is made up of individuals and that there is no such thing as “The” law, just interpretations of it.
Any Justice can join in full or in part any other decision, and issue a concurrence and/or dissent to clarify differences. Sometimes a Justice will circulate a draft opinion and solicit changes in hopes of getting more to join it.
The OP might find it interesting to read the passages of The Brethren, in relation to two cases in particular: United States v. Nixon ( the tapes case) and Gregg v. Georgia, the death penalty case discussed in the final chapter of the book. There was considerable horse-trading going on with both of those cases. In Nixon, it resulted in a unanimous decision against the President, and in Gregg, the centrist judges controlled the final outcome.
A more recent example is in Toobin’s book, The Nine. He gives a behind-the-scene account of the development of the majority decision in Planned Parenthood v. Casey, which altered the Roe v. Wade framework somewhat, while upholding the basic points of that case.
Just checking to see that the link to Casey doesn’t take you to Popular Mechanics on 9/11.
Good, it doesn’t. 