The Consecutive-Ones Property (C1P) is a classical concept in discrete mathematics that has been used in several genomics applications, from physical mapping of contemporary genomes to the assembly of ancient genomes. A common issue in genome assembly concerns repeats, genomic sequences that appear in several locations of a genome. Handling repeats leads to a variant of the C1P, the C1P with multiplicity (mC1P), that can also be seen as the problem of covering edges of hypergraphs by linear and circular walks. In the present work, we describe variants of the mC1P that address specific issues of genome assembly, and polynomial time or fixed-parameter algorithms to solve them.