The matroid rank conjecture for Hadamard products of linear spaces

Let $L_1,\dots,L_d \subseteq \mathbb{R}^E$ be finite-dimensional linear spaces, and let $M_1,\dots,M_d$ be their algebraic matroids. Write $r_{M_i}$ for the rank function of $M_i$, and let $\star$ denote the Hadamard product of linear spaces. Hadamard-product matroid conjecture.

$$\mathcal{M}(L_1\star\dots\star L_d)=\mathcal{M}(r_{M_1}+\dots+r_{M_d}-d+1).$$

This conjecture would generalize the preceding theorem from Hadamard products of two linear spaces to products of an arbitrary finite number of linear spaces. The source does not state a resolution, so the conjecture remains open.