Targeting urban and sub-urban building archetypes, generic but practice-oriented materializations of basic construction elements (slabs and walls) and their combinations were conceived for heightening of existing buildings by two to four floors. The developed concepts considered numerous construction materials and requirements from architecture, structural engineering, building physics, and fire protection. Evaluations explored the effects on embodied carbon, weight and estimated cost per surface unit of market-oriented element combinations, to identify suitable (and inappropriate) materializations and to detect governing elements and materials. Globally, a heightening by four floors is better than by two, in terms of relative carbon and cost impacts, but some trade-offs in architectural floor plan layout may be required. Seeking cost reductions is generally disadvantageous for embodied carbon while an investment increase does not necessarily provide a reduced carbon footprint. Overall, timber construction results in the lowest embodied carbon (around 5 kg CO2,eq/m2·a) while being up to 10% more expensive than the cheapest and up to 15% heavier than the lightest materializations (which depend on the floor plan layout). Lightweight concrete construction can be the most economic materialization but is also up to 200% heavier than the lightest (which can possibly not be supported by the existing building), and results in up to 45% more embodied carbon than constructing with timber.