Every closed flat 3-manifold is realized as a cusp section of a cusp-transitive finite-volume hyperbolic 4-manifold; dense subsets of flat metrics on each such 3-manifold are also realizable, and many 4-manifolds exist with pairwise isometric cusps of any given type.
Cusps of hyperbolic 4-manifolds and rational homology spheres
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Cusp-transitive 4-manifolds with every cusp section
Every closed flat 3-manifold is realized as a cusp section of a cusp-transitive finite-volume hyperbolic 4-manifold; dense subsets of flat metrics on each such 3-manifold are also realizable, and many 4-manifolds exist with pairwise isometric cusps of any given type.