The conjecture on reducing matroids to partition matroids

Let $M$ be a $k$-colorable matroid, meaning that its ground set can be partitioned into $k$ independent sets. A reduction to a partition matroid is a partition matroid on the same ground set whose independent sets are also independent in $M$. Reduction conjecture. Every $k$-colorable matroid can be reduced to a $2k$-colorable partition matroid. The paper presents this as a conjectural extension of its reductions for several classes, including gammoids; the general case is not established in the supplied text.