Thanks @NCP it is working as you described but unfortunately not in the way I had hoped.
I was looking at the inverse, so that a specific item were only bought from specific suppliers rather than specific suppliers are very restricted in what we can buy from them.
i.e. we have to buy certain chemicals of a specific grade from our supplier, an item we would want to make Party Specific. But we also buy various other chemicals from this supplier and other suppliers (depending on price/availability) which have no restriction on purchase. So as it stands Party Specific Item does not work in this way.
I’ll maybe change the bug report to a feature request to allow this.