You are mixing up vocabulary. Duplication means that the exact same DNA fragment (or at least a fragment with the same start and end coordinate) has been sequenced multiple times. In experiments like ChIP, we typically remove them to avoid counting technical artifacts that would inflate the actual counts within a region. Reads aligning more than once are a completely different thing. It means that a given DNA sequence occurs more than once in the genome. This can happen because the fragment comes from a repetitive region, such as a telomer or centromer, or comes from paralog genes, that share high sequence similarity. Still, using reads only aligning once and removing duplicates is fine, and you may proceed with your analysis.