A mineralogical mapping (terrain analysis) based on micro-mounts has been performed in the Archipelago of the Canary Islands, Spain. The rare elements Be, F, Li, Nb, Ta, Zr, Hf, and rare earth elements (REE) were investigated on the largest island of the Canary Islands Archipelago, Tenerife, Spain. This study forms a contribution to the metallogenetic evolution of the offshore area of the NW African Rare Mineral Province. The finds made at Tenerife were correlated by means of minero-stratigraphy with the adjacent islands La Gomera, Gran Canaria and Fuerteventura, where typical critical element host rocks, e.g., carbonatites, are exposed. At Tenerife, these hidden rock types are only indicated by a wealth of 128 compositional first-order marker minerals hosting Be, F, Zr, Nb, Ta, Zr, Hf, Li, Cs, Sn, W, Ti and REE plus Y and another 106 structural second-order marker minerals describing the geodynamic and morpho-structural evolution of Tenerife (Mn, Fe, Pb, U, Th, As, Sb, V, S, B, Cu, Zn, Mo, Au). Based upon the quantitative micro-mineralogical mapping of lithoclasts and mineralogical xenoliths (foid-bearing monzodiorite/gabbro, (nepheline) syenite, phonolite trachyte) in volcanic and volcaniclastic rocks, hidden intrusive/subvolcanic bodies can be delineated that are associated with contact-metasomatic, zeolitic and argillic alteration zones, as well as potential ore zones. Two potential types of deposits are determined. These are pegmatite-syenites with minor carbonatites bound to a series of agpaitic intrusive rocks that are genetically interlocked with rift zones and associated with a hotspot along a passive continental margin. Towards the east, the carbonatite/alkali magmatite ratio reverses at Fuerteventura in favor of carbonatites, while at Gran Canaria and La Gomera, shallow hypogene/supergene mineral associations interpreted as a marginal facies to Tenerife occur and a new REE discovery in APS minerals has been made. There are seven mineralizing processes different from each other and representative of a peculiar metallogenic process (given in brackets): Protostage 1 (rifting), stages 2a to 2d (differentiation of syenite–pegmatite), stages 3 to 4b (contact-metasomatic/hydrothermal mineralization), stages 5a to 5b (hydrothermal remobilization and zeolitization), stage 6 (shallow hypogene-supergene transition and kaolinization), and stage 7 (auto-hydrothermal-topomineralic mineralization). The prerequisites to successfully take this holistic approach in economic geology are a low maturity of the landscapes in the target area, a Cenozoic age of endogenous and exogenous processes amenable to sedimentological, geomorphological, volcano-tectonic and quantitative mineralogical investigations. The volcanic island’s mineralogical mapping is not primarily designed as a proper pre-well-site study on the Isle of Tenerife, but considered a reference study area for minero-stratigraphic inter-island correlation (land–land) and land–sea when investigating the seabed and seamounts around volcanic archipelagos along the passive margin, as exemplified by the NW African Craton and its metallogenic province. This unconventional exploration technique should also be tested for hotspot- and rift-related volcanic islands elsewhere on the globe for mineral commodities different from the ones under study.