People may choose not to drink from the cup for a number of reasons. For example, they may not want to drink after the many people who have drank before them or they may not want others to drink after them. Choices such as these would not be matters of “a lack of faith” but rather a concern for health – one’s own health or the health of others. The transubstantiated blood retains the accidents of wine and can be contaminated similarly. “Christ is present whole and entire in each of the species” (Catechism of the Catholic Church, 1377) so one may fully partake of the Eucharist by receiving only the body.
Administration of the Eucharist by dipping the body into the blood is known as intinction. This is an acceptable practice as is the use of multiple cups.