I will present the new opportunities offered by the proposed general-purpose intensity-frontier experimental facility BDF/SHiP that is aimed at operating in beam-dump mode in the existing SPS ECN3 experiment underground area. The proposal is part of the ongoing decision process at CERN that is focused on the beyond-LS3 physics program in ECN3, and that should come to conclusion by the end of 2023. The SHiP experiment aims to search for feebly interacting GeV-scale particles and perform measurements in neutrino physics. BDF/SHiP complements the worldwide program of New Physics searches by exploring a large region of parameter space that cannot be addressed by other experiments, and which reaches several orders of magnitude below existing bounds by efficiently exploiting the currently available 4x10^19 protons per year at 400 GeV for up to 10-15 years. The SHiP experiment has generic sensitivity to decay and scattering signatures of models with feebly interacting particles, such as dark-sector mediators and light dark matter. In neutrino physics, BDF/SHiP can perform unprecedented measurements with tau neutrinos and neutrino-induced charm production. This proposal benefits from the extensive studies undertaken for the Technical Proposal submitted in 2015 and the subsequent Comprehensive Design Study (CDS) of BDF/SHiP located at a new beamline at the CERN SPS.