You can ask to avoid stuff. You can ask to actively go to other places. But if it’s just not possible to build you a complete roster, taking those requests into account, then you’ll then be given anything, and it will obviously have to be stuff you asked to avoid or didn’t ask to go to.
(There is indeed a command which blocks reports before a certain time. But if by the time JSS gets to you, there are only early reports remaining, it’s not going to say “OK mate, I won’t give you any work because you don’t want those early reports.” So you can put in your preferences using a whole host of conditions, but the chances of you getting everything you’ve asked for depends on your relative seniority, and the kind of stuff you’ve asked for.)