CERN has launched a study phase to evaluate the feasibility of a new high-intensity beam dump facility at the CERN Super Proton Synchrotron accelerator with the primary goal of exploring Hidden Sector models and searching for Light Dark Matter, but which also offers opportunities for other fixed target flavour physics programs such as rare tau lepton decays and tau neutrino studies. The new facility will require - among other infrastructure - a target complex in which a dense target/dump will be installed, capable of absorbing the entire energy of the beam extracted from the SPS accelerator. In theory, the target/dump could produce very weakly interacting particles, to be investigated by a suite of particle detectors to be located downstream of the target complex. As part of the study, a development design of the target complex has been produced, taking into account the handling and remote handling operations needed through the lifetime of the facility. Two different handling concepts have been studied and both resulting designs are presented.