Impact craters that form on every planetary body provide a record of planetary surface evolution. On heavily-cratered surfaces, new craters that form often overlap older craters, but it is unknown how the presence of older craters alters impact crater formation. We use overlapping complex crater pairs on the lunar surface to constrain this process and find that crater rims are systematically lower where they intersect antecedent crater basins. However, the rim morphology of the new crater depends on both the depth of the antecedent crater and the degree of overlap between the two craters. Our observations suggest that transient rim collapse is altered by antecedent topography, leading to circumferential distribution of rim materials in the younger crater. This study represents the first formalization of the influence of antecedent topography on rim morphology and provides process insight into a common impact scenario relevant to the geology of potential Artemis landing sites.