So I've been trying to find an answer to this question, but couldn't be certain, because either the information that I found is simply over my head, or from 2 to 3 years ago, so possibly no longer relevant.
On my stock Android, I'm using a Visible SIM. If I go to edit APN settings, there's usually a big "plus" button for adding a new APN, which you can then select, instead of the default APN. I have this option available for other SIM's, but not for Visible.
For those of you running Visible on Graphene, are you able to add custom APN's to your phones? Do you see the option to add an APN available is that part of the settings menu?