What's the procedure for Supreme Court to reschedule a case to decide if to grant cert?

[NewYorkExpress]

It's not out of the realm of possibility, I suppose, that at least one of the justices on the opposite side (such as a conservative judge on Civil Rights issue in the Warren Court, or a liberal judge in an abortion issue in this court) might grant in a high profile case just to get their fellow justices's positions on the record in an oral argument, but that doesn't seem like something our current liberal trio of justices would do.

[NewYorkExpress]

Why do they do this? And in the civil right era, there were pretty much only two reliable conservative until 1991.

I just said why. They'd want their fellow justices positions on the record in Oral Arguments. Especially in this day and age, pretty much everything, even the supposedly impartial Supreme Court, is political.

[NewYorkExpress]

How would having "their fellow justices positions on the record " help them?

A lot of oral arguments are public now, with an audience (which may or not include the press). There often is a record of said oral argument.

Having a justice's position on a subject could be helpful for a justice's party, especially when confirming future justice's or, as we've realized, impeachment is going to be merely about political views and not about actual crimes.