The search for exploitable deposits of water and other volatiles at the Moon's poles has intensified considerably in recent years, due to the renewed strong interest in lunar exploration. With the return of humans to the lunar surface on the horizon, the use of locally available resources to support long-term and sustainable exploration programs, encompassing both robotic and crewed elements, has moved into focus of public and private actors alike. Our current knowledge about the distribution and concentration of water and other volatiles in the lunar rocks and regolith is, however, too limited to assess the feasibility and economic viability of resource-extraction efforts. On a more fundamental level, we currently lack sufficiently detailed data to fully understand the origins of lunar water and its migration to the polar regions. In this paper, we present LUVMI-X, a mission concept intended to address the shortage of in situ data on volatiles on the Moon that results from a recently concluded design study. Its central element is a compact rover equipped with complementary instrumentation capable of investigating both the surface and shallow subsurface of illuminated and shadowed areas at the lunar south pole. We describe the rover and instrument design, the mission's operational concept, and a preliminary landing-site analysis. We also discuss how LUVMI-X fits into the diverse landscape of lunar missions under development.