Store serving platters and oversized serving pieces upright in a sturdy organizer with dividers, similar to the organizers used for baking sheets. An expandable model with adjustable dividers is especially useful because serving pieces vary so much in size.
Start with what you already own and how often you use it. Edit first, then choose a home for each category and buy additional storage only if there is a genuine gap.
My final check is practical: can you find what you need quickly, put it back just as easily, and see when the space is getting full? If not, simplify the categories or move the storage closer to where you use it. An organizing system should make life easier, not become another chore.
Mr. Organized's Answer