Yes, you can decline individual prizes. For example, if the prize package is a dining room with dinnerware, the collection of dining room furniture is treated as one prize and the collection of dinnerware is treated as a separate prize. A winning contestant could choose to decline just the furniture or just the dinnerware.
A winning contestant cannot accept only part of what makes up an individual prize, though. So, for example, a contestant could not choose to accept only the table and four of the six chairs while declining the hutch -- it's all of the furniture that was in the manufacturer's prize plug or nothing. Similarly, if a contestant wins four Kate Spade handbags, they have to accept all four or none at all -- they can't choose to take only one or two of the handbags.