Different outcomes in the parameter space of tight triples, with arbitrary tertiary mass (m₃) and outer orbital period (P_out), that host inner binaries whose component stars undergo CHE. At the ZAMS, the system includes an inner circular binary with masses m₁=m₂ = 55 M_⊙ and an orbital period of 1.1 d, at a metallicity of Z = 0.00042. We use different colours to highlight various regions of interest. Dark grey indicates dynamically unstable triples. Grey and light grey represents the region where von Zeipel-Kozai-Lidov (ZLK) oscillations can lead to prompt hydrogen-rich and helium-rich stellar mergers in the inner binary, respectively. The colour bar gradient illustrates how ZLK oscillations can decrease the time-to-coalescence via gravitational-wave emission (τ_merge,min), potentially reducing it to the ZLK timescale (cf. Fig. 4). Wide triples (P_out≳1000 d) remain unperturbed, with the inner binary evolving into a BBH that can merge in approximately 450 Myr (Sect. 2.1.1). The vertical dashed red line marks the mass where m₃=m_1,ZAMS, roughly delineating systems where the tertiary may evolve more rapidly than either of the inner binary components, potentially leading to a tertiary mass-transfer episode.