Can a person receive the consecrated host and then dip it in the chalice to receive the consecrated wine?

What you describe is a practice known as self-intinction. Self-intinction is strictly forbidden. At the Last Supper the invitation that Christ gave to the Apostles and gives to us at the celebration of the Eucharist is: “Take and eat. This is my body.” “Take and drink. This is my blood poured out for you…” The Eucharist we receive is truly the body, blood, soul and divinity of Christ. It is no longer bread and wine. In receiving it by eating and drinking we are called to become the Body of Christ pouring out ourselves for others.