Splitting links by integer homology spheres

For every n ≥ 3, we construct 2-component links in S^n+1 that are a split by an integer homology n-sphere, but not by S^n. In the special case n=3, i.e. that of 2-links in S^4, we produce an infinite family of links L_ℓ and of integer homology spheres Y_ℓ such that the link L_ℓ is (topologically or smoothly) split by Y_ℓ and by no other integer homology sphere in the family.