Simply select a couple of the consecutive paragraphs, then use the boders tool to apply an internal border (click on Borders & Shading>Borders, then the middle of the three buttons on the Preview panel). Having done that, select each paragraph in turn, then update the Style to match the selection. You might want to specify a different internal border format than what you're using for the outside borders.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]