  Let $M$ be a matroid satisfying a matroidal analogue of the Cayley-Bacharach
condition. Given a number $k \ge 2$, we show that there is no nontrivial bound
on ranks of a $k$-tuple of flats covering the underlying set of $M$. This
addresses a question of Levinson-Ullery motivated by earlier results which show
that bounding the number of points satisfying the Cayley-Bacharach condition
forces them to lie on low-dimensional linear subspaces. We also explore the
general question what matroids satisfy the matroidal Cayley-Bacharach condition
of a given degree and its relation to the geometry of generalized permutohedra
and graphic matroids.
