@SamHopkins Thanks for the insights. Are there any references on multi-arrangements?

My knowledge of the implications of the foregoing semigroup relationship is quite limited to make a judgement on this.

I'll also note that there is some relationship between the Tits semigroup of an affine arrangement and subsemigroup of the cone of the arrangment, but is this enough to use a large majority of the results in the field? eg. JKS isomorphism etc.