System for supplying a substance

System for supplying a liquid or paste-like substance, comprising:

• a compressible bag for receiving the substance to be supplied;
• a supply assembly which forms a supply channel with a corresponding supply mouth for supplying the substance from the bag;
• a container with a supporting body at least comprising a supporting plate and with a movable presser plate, wherein the supporting body and the presser plate together form a chamber for the incorporation therein of the bag, so that the bag is positioned between the supporting plate and the presser plate, wherein the presser plate can be moved in a pressure direction to the supporting plate to force the substance from the bag;
• wherein the supporting body in a region between the supporting plate and the presser plate is provided with a passage for the supply assembly;
• wherein the presser plate on one of its edges and the supporting body are provided connecting means working in concert, which edge of the presser plate is situated away from the supply assembly;
• and wherein the connecting means, viewed in the pressure direction, provide several possible connecting positions of the presser plate and the supporting body, such that when the bag is emptied, the connecting position effectively taken up by the connecting means is moved closer to the supporting plate.