The EF1 conjecture for matroids with heterogeneous valuations

Let $M=(E,\mathcal{I})$ be a matroid on the finite set of goods $E$, and let $\chi(M)$ be the least number of independent sets in a partition of $E$. Suppose $\chi(M)\leq n$ and there are $n$ agents with additive valuations $v_1,\ldots,v_n$. The heterogeneous matroid EF1 conjecture. There exists an EF1 partition of $E$ into $n$ independent sets of $M$. This is presented as a stronger version of the common-valuation matroid conjecture, and the source does not report a proof or disproof.