Strict separation of recursively, divisionally and multiplicatively free arrangements

Let $\mathcal{RF}^*$ denote the class of recursively free arrangements satisfying the additional condition denoted by a star in the source, let $\mathcal{DF}$ denote the class of divisionally free arrangements, and let $\mathcal{MF}$ denote the class of multiplicatively free arrangements. Based on examples, the recursively free arrangement conjecture.

$$\mathcal{RF}^*\subsetneq\mathcal{DF},\qquad \mathcal{RF}\subsetneq\mathcal{MF}.$$

These strict inclusions assert that the indicated classes are properly distinct. The source presents both inclusions as conjectural; the notation $\mathcal{RF}^*$ and the precise definition of the starred class should be checked against the paper.