Deformation structures in the wall rocks of igneous intrusions emplaced at shallow crustal depths preserve an important record of how space was created for magma in the host rocks. Trachyte Mesa, a small Oligocene age intrusion in the Henry Mountains, Utah, is composed of a series of stacked tabular, sheet-like intrusions emplaced at 3–3.5 km depth into sandstone-dominated sedimentary sequences of late Palaeozoic–Mesozoic age. New structural analysis of the spatial distribution, geometry, kinematics and relative timings of deformation structures in the host rocks of the intrusion has enabled the recognition of distinct pre-, syn-, and late-stage-emplacement deformation phases. Our observations suggest a two-stage growth mechanism for individual sheets where radial growth of a thin sheet was followed by vertical inflation. Dip-slip faults formed during vertical inflation; they are restricted to the tips of individual sheets due to strain localisation, with magma preferentially exploiting these faults, initiating sill (sheet) climbing. The order in which sheets are stacked impacts on the intrusion geometry and associated deformation of wall rocks. Our results offer new insights into the incremental intrusion geometries of shallow-level magmatic bodies and the potential impact of their emplacement on surrounding host rocks.