Common Variability Language (CVL) is a generic variability modeling language. Fragment substitution is a fundamental CVL operation. The operation removes a set of model elements (placement fragment) and substitutes them with another set of elements (replacement fragment). Overlapping fragments represent a potential consistency challenge as the CVL execution may give unintended results for models where fragments intersect. Thus, we argue that there is a pragmatic need to handle overlapping placements. The need emerges, when several diagrams reference the same model. Hence, we can define a placement in one diagram while another placement in a different diagram references the same set of elements. It may indicate an error in the variability definition, but there are cases where we specify overlapping placements intentionally. In the thesis we carefully discuss such cases, 1) classify overlapping fragments, 2) find criteria to detect the different overlaps, and 3) suggest appropriate solutions via transformations.