In this work, using our range-resolved interferometry (RRI) signal processing technique, we present a novel approach to multidimensional displacement measurements using only a single optical access port and very simple optical setup. By utilising surface reflections from a stage-mounted moving beamsplitter and two orthogonal stationary reference mirrors, two interferometers for the two Cartesian measurement directions are formed. With RRI, the interferometric phase signals of both interferometers can be independently demodulated, allowing simultaneous measurements of displacement in both dimensions using a single continuous-wave laser diode source and a single photodetector. In this paper, the capabilities of this approach are demonstrated using a proof-of-concept experiment with a multidimensional Piezoelectric stage performing a variety of stage movements. Measurements of displacements over a nominal stage working range of ±50μm are presented, demonstrating independent, simultaneous displacement measurements of two dimensions. The presented measurements show nanometer-level displacement resolutions with typical noise densities of 0.02 nm/√Hz over a 21 kHz bandwidth. It is thought that this approach could offer an interesting alternative to existing interferometric techniques for multi-dimensional metrology, benefiting from both simplicity and cost-effectiveness whilst maintaining the advantages that make optical techniques attractive to scientific and industrial applications.