Method and apparatus for forming both carafe quantities and smaller (e.g., cup) quantities of a beverage using a cartridge-based beverage machine. A beverage forming machine accommodates cartridges having different sizes and/or shapes, including different rim sizes/shapes. The outlet used for receiving a beverage from a standard cartridge differs from the outlet used for receiving the beverage from a carafe cartridge inserted in a same cartridge holder. Beverage may exit the cartridge in an upward direction in some embodiments.