Household cleaning appliance with a non-bulk dispensing system convertible to a household cleaning appliance with a bulk dispensing system

A treating chemistry dispensing system for an appliance having a treating chamber, comprising:

• a non-bulk dispensing system including a set of walls forming a dispensing cup configured to be fluidly coupled with the treating chamber and dispense an entirety of a dose located within the dispensing cup and wherein a portion of one of the set of walls is configured to be removed to create an opening in the one of the set of walls and wherein the non-bulk dispensing system is configured to receive at least a portion of a removable cartridge containing a treating chemistry that is fluidly coupled to the treating chamber via the opening when the portion is removed and the removable cartridge is received in the non-bulk dispensing system.