We present measurements of relative elemental abundances in plumes and interplumes. Plumes are bright, narrow structures in coronal holes that extend along open magnetic field lines far out into the corona. Previous work has found that in some coronal structures the abundances of elements with a low first ionization potential (FIP) <10 eV are enhanced relative to their photospheric abundances. This coronal-to-photospheric abundance ratio, commonly called the FIP bias, is typically 1 for elements with a high-FIP (>10 eV). We have used Extreme Ultraviolet Imaging Spectrometer observations made on 2007 March 13 and 14 over a ≈24 hr period to characterize abundance variations in plumes and interplumes. To assess their elemental composition, we used a differential emission measure analysis, which accounts for the thermal structure of the observed plasma. We used lines from ions of iron, silicon, and sulfur. From these we estimated the ratio of the iron and silicon FIP bias relative to that for sulfur. From the results, we have created FIP-bias-ratio maps. We find that the FIP-bias ratio is sometimes higher in plumes than in interplumes and that this enhancement can be time dependent. These results may help to identify whether plumes or interplumes contribute to the fast solar wind observed in situ and may also provide constraints on the formation and heating mechanisms of plumes.