The subject of the invention is the house developable upwards and the system of its extension. The house developable upwards that already at the design stage is adapted to the subsequent investment cycle, characterised by the fact, that after the first stage of building process the load-bearing structure of the building in the vertical intersection has got the shape of the 'H&rdguo; or 'h&rdquo,- letter or the shape close to them, and the horizontal line (2) is the line of the structural ceiling and/or a flat roof and/or a roof, below which there is situated the top and roofed-over closed storey, and above there is at least one load-bearing wall (1) or load-bearing structure forming a shield- for an optional terrace, and/or a garden situated on the roof, and/or a shield for the roofed over open storey, and/or a shield for the empty space over the roof, at the some time the load-bearing wall or the load-bearing (1) structure protruding above the built-over storey form an element binding the elements added on the top to the load-bearing structure of the building at the next stage of the construction process.