William’s Ridge, a ~300-km-long salient extending southeast from the Central Kerguelen Plateau, and Broken Ridge are conjugate divergent margins in the southern Indian Ocean that separated at ~43 Ma. In early 2020, scientists aboard Australia’s Marine National Facility, RV Investigator, acquired multichannel seismic reflection (MCS), sub-bottom profiling, multibeam bathymetry, and gravity data on these margins, as well as dredged rock samples, on a 57-day voyage. The research project constitutes the first-ever case study of conjugate oceanic plateau end-member tectonic plates, with the goal of advancing knowledge of lithospheric rifting, breakup, and initial plate separation processes. The first-ever dedicated multibeam mapping of William’s and Broken ridges encompassed ~52,000 km2 and ~43,000 km2, respectively. Four new RV Investigator MCS profiles (500 line-km) across William’s Ridge complement one legacy RV Rig Seismic and three new RV Sonne MCS profiles; five new RV Investigator MCS profiles (603 line-km) across the conjugate portion of Broken Ridge are the first to be acquired on that feature. Multibeam bathymetry and MCS transects of William’s Ridge show multiple linear ridges and troughs interpreted as horst and graben. In contrast, multibeam bathymetry and MCS transects of Broken Ridge show a prominent E-W scarp (Diamantina Escarpment) with a complex morphology of emanating en echelon crustal blocks and depressions at the base of the scarp. Prominent angular unconformities (middle Eocene hiatus?) characterize the sedimentary section on some ridges, and dipping reflection sequences within interpreted igneous basement suggest subaerial basalt flows. Rock dredges on the facing conjugate margin fault scarps targeted all stratigraphic levels exposing basement rocks. Nine on William’s Ridge yielded both oceanic and (in situ?) continental rocks; eight on Broken Ridge yielded solely oceanic rocks. The new geophysical data and geological samples may justify a new or revised submission to the United Nations Commission on the Limits of the Continental Shelf to extend Australia’s marine jurisdiction on and around William’s Ridge under the United Nations Convention on the Law of the Sea.