  In 2007, Cochran-Friedl-Teichner gave sufficient conditions for when a
multi-infection link is topologically slice involving a Milnor's invariant
condition on the infecting string link. In this paper, we give a different
Milnor's invariant condition which can handle some cases which the original
theorem cannot. Along the way, we also give sufficient conditions for a
multi-infection to be $(n-0.5)$-solvable, where we require that the infecting
string link have vanishing pairwise linking numbers, which can be seen as
handling an additional ``$(-0.5)$-solvable'' case of a well-known result about
the relationship between satellite operations and the solvable filtration of
Cochran-Orr-Teichner.
