The origin, environment, and evolution of stellar-mass black hole (BH) binaries are still a mystery. One of the proposed binary formation mechanisms is manifest in dynamical interactions between multiple BHs. A resulting framework of these dynamical interactions is the so-called hierarchical triple-merger scenario, which happens when three BHs become gravitationally bound, causing two successive BH mergers to occur. In such successive mergers, the BHs involved are directly related to each other, and hence this channel can be directly tested from the properties of the detected binary BH mergers. Here we present a search for hierarchical triple mergers among events within the first and second gravitational-wave transient catalogs of the Laser Interferometer Gravitational-Wave Observatory/Virgo, the eccentric localization of GW190521, and those found by the IAS-Princeton group. The search includes improved statistical quantification that also accounts for BH spins. We perform our analysis for different upper bounds on the mass distribution of first-generation BHs. Our results demonstrate the importance of the mass distributions' properties for constraining the hierarchical merger scenario. We present the individually significant merger pairs. The search yields interesting candidate families and hints of its future impact.