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very difficult without seeing the room but if they are really built in why not run a batten along the back of each shelf. If they're more than 4 feet long you'll need intermediate brackets of some kind, or you could have slotted uprights the same depth as the shelves, and slot (halve-joint or " eggbox") them together. If you eggbox the whole thing then you'd only need to put a batten under the middle and top shelves, to stop the whole lot falling forward. I love jobs like that.
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