An ostomy coupling including a body-side coupling member, an appliance-side coupling member including plural fastener lugs, and a bracing member. The lugs flex independently of each other to provide plural independent latching fastenings. The bracing member is moved between a bracing position in which the bracing member locks the lugs by resisting flexing movement, and a non-bracing or dismounted position in which the lugs are free to flex. The ostomy coupling is used with an ostomy pouch or with a controlled evacuation device.