  We construct finitely generated torsion-free solvable groups $G$ that have
infinite rank, but such that all finitely generated torsion-free metabelian
subquotients of $G$ are virtually abelian. In particular all finitely generated
metabelian subgroups of $G$ are virtually abelian. The existence of such groups
shows that there is no "torsion-free version" of P. Kropholler's theorem, which
characterises solvable groups of infinite rank via their metabelian
subquotients.
