An appliance for making a drink individually. The appliance includes a plurality of containers. Each container includes a vessel and a head screwed onto the vessel. A base defines a plurality of housings each receiving a container, and being provided with a housing outlet and a pressurizing inlet connected with a drain valve and a pressurizing valve of the container, respectively. A funnel is mounted under the housing outlets. Structure transfers by pressurization, into the funnel, ingredients contained in the containers housed in the housings. The vessel and the head of at least one container include polarizing surfaces of the vessel and of the head, respectively, configured to form, together, a container polarizing surface that can cooperate with a housing polarizing surface to ensure a predetermined positioning of the container with respect to the housing.