A structural collapse transition induced by pressure or strain is ubiquitous among the ThCrSi-type Fe-based pnictides and dramatically affects their magnetic, superconducting, and elastic properties. The recently discovered CaKFeAs, belonging to the 1144-type compounds, shows two separate half-collapsed tetragonal (hcT) transitions where As-As bonds form across different layers at distinct critical pressures. The present work uses state-of-the-art first-principles simulations to predict the hcT transitions and reveal general trends for all known 1144 pnictides, including the ferromagnetic superconductors EuRbFeAs and EuCsFeAs. In the Eu-based systems, magnetism of the localized 4 electrons appears to be stable across both hcT transitions, while the magnetic pattern may be affected by pressure.