Surface systems of links and refined triple linking numbers

A surface system for a link in the 3-sphere is a collection of Seifert surfaces for the components of the links, that intersect one another transversally and in at most triple points.  The intersections are thought of as oriented manifolds.  Given two links with the same pairwise linking numbers, do they admit homeomorphic surface systems?

I will explain how this question can be answered using a refined version of Milnor's triple linking numbers.  This question also relates to bordism of the link exteriors over the free abelian group, and lower central series quotients of the link groups.  This is joint work with Chris Davis, Matthias Nagel and Patrick Orson.