Final answer:
Oxygen is the element that, like carbon and nitrogen, can form multiple covalent bonds by sharing pairs of electrons with other atoms to complete its valence shell.
Step-by-step explanation:
The question 'Multiple covalent bonds may occur in atoms that contain carbon, nitrogen, or...?' is seeking another element that is capable of forming multiple covalent bonds, similar to carbon and nitrogen. The answer to this question is oxygen. Like carbon and nitrogen, oxygen is also known to form multiple covalent bonds, such as single and double bonds, due to its ability to share two pairs of electrons with other atoms to complete its valence shell.
For example, in the formation of water molecules (H2O), two covalent bonds are formed between one oxygen atom and two hydrogen atoms. Additionally, the oxygen molecule (O2) consists of a double bond (O=O), which clearly illustrates oxygen's capacity to form multiple covalent bonds with itself and other elements.