At this particular stage we don't have to "amend" the constitution, as an internet bill would be, generally speaking, global (if the rights only applied to America, it would defeat the point of it being a bill for the internet).
As someone outside America, I have a very strong interest in ensuring IBOR succeeds globally, because it's the kind of protections myself and others cannot presently enjoy (police arresting people for making twitter bomb jokes whilst allowing pedophiles to go scot-free in Rotherham is the biggest fucking outrage in a century and not a single complaint from anyone anywhere).
If enough countries adopt or ratify IBOR (I'm hoping EU gets on board because once they adopt it, it will force pretty much everyone else to do so as well), it would become de facto.
It might not be in the constitution, but I think IBOR reinforces the American constitution nicely (both support freedom of speech, and I bet a judge would argue freedom of speech on the internet is hypothetically covered by said pre-existing constitution).
Adding it to the constitution might not be possible, but if we could shore it up to be difficult to assail as Section 230 was and have it unilaterally enforced by other countries (so it 'overlaps'), not only would this allow freedom of speech for individuals like myself, but also for those in countries who have no voice to start speaking out.
Otherwise, one of your major issues is companies will move overseas in order to avoid complying with IBOR, like they already do with GDPR for countries outside the EU.