If you're talking about the QuickAdd that gets downloaded from the User Self Enrollment page, I'm not sure there's a way to do that. Those are single use packages and I'm not sure if there are settings to modify that.

OTOH, you can create a multi use QuickAdd.pkg from Recon.app.

You can do a Multiple QuickAdd with a time bomb by going into your jss'es admin page and then going to Enrollment Invitations, send an invite to yourself, as you walk through the wizard you'll see under "security" the option to set a time, multiple uses etc.

You could check out making one with the Recon app as well. You can definitely enroll more than one device, not sure if you can make it expire though.