I broadly agree with this but it raises a bigger question -- how do you punish someone who is already in a process of punishment?

That's an especially important question when someone is going through a very long punishment process, like what does another life sentence mean to someone who has a life sentence? You can't execute someone twice, right?

If someone breaks a very important rule in prison there needs to be some way to put an immediate stop to that behaviour and to disincentivize them from doing it again and in a situation like this is seems like solitary confinement is the most effective way to do that.