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Recent detections of gravitational waves from mergers of neutron stars (NSs)and black holes (BHs) in the low and high-end mass gap regimes pose a puzzle tostandard stellar and binary evolution theory. Mass-gap mergers may originatefrom successive mergers in hierarchical systems such as quadruples. Here, weconsider repeated mergers of NSs and BHs in stellar 2+2 quadruple systems, inwhich secular evolution can accelerate the merger of one of the inner binaries.Subsequently, the merger remnant may interact with the companion binary,yielding a second-generation merger. We model the initial stellar and binaryevolution of the inner binaries as isolated systems. In the case of successfulcompact object formation, we subsequently follow the secular dynamicalevolution of the quadruple system. When a merger occurs, we take into accountmerger recoil, and model subsequent evolution using direct N-body integration.With different assumptions on the initial properties, we find that the majorityof first-generation mergers are not much affected by secular evolution, withtheir observational properties mostly consistent with isolated binaries. Asmall subset shows imprints of secular evolution through residual eccentricityin the LIGO band, and retrograde spin-orbit orientations. Second-generationmergers are ~10^7 times less common than first-generation mergers, and can bestrongly affected by scattering (i.e., three-body interactions) induced by thefirst-generation merger. In particular, scattering can account for mergerswithin the low-end mass gap, although not the high-end mass gap. Also, in a fewcases, scattering could explain highly eccentric LIGO sources and negativeeffective spin parameters.

First and second-generation black hole and neutron star mergers in 2+2 quadruples: population statistics