This paper aims to expand understanding of a poorly known group of cestodes that parasitize an intriguingly diverse suite of elasmobranchs. The group's three currently described members (i.e., Pentaloculum macrocephalum, Pentaloculum hoi, and Zyxibothrium kamienae) parasitize an electric ray, a carpet shark, and a skate, respectively. Pentaloculum grahami n. sp. is described from a second genus of carpet shark, specifically Parascyllium collare, in Australia. Zyxibothrium duffyi n. sp. and Zyxibothrium healyae n. sp. are described from the deep-sea skates Brochiraja asperula and Brochiraja spinifera, respectively off New Zealand. The three new species share distinctive bothridia that bear a small number of large, circular, facial loculi and lateral bands of vitelline follicles that converge posterior to the ovary-features which are found in all other members of these genera. Zyxibothrium healyae n. sp. is unique in possessing three, rather than four or five, facial loculi. Zyxibothrium duffyi n. sp. possesses a combination of five facial loculi and vitelline follicles that stop short of the anterior margin of the proglottid. Pentaloculum grahami n. sp. is the largest member of the group with the greatest number of proglottids. Based on striking similarities in scolex morphology, Pentaloculum and Zyxibothrium have been hypothesized to belong to a distinct subgroup of "tetraphyllideans" provisionally designated as Clade 1. Based on sequence data for the D1-D3 region of the 28S rDNA gene generated for species of Zyxibothrium for the first time, we confirm the reciprocal monophyly of both genera as well as the monophyly of Clade 1 and its status as a distinct lineage among the "Tetraphyllidea". This work also suggests that the presence of five facial loculi is homoplasious given this character state is found in members of both genera. The new species expand the host associations of Clade 1 to include additional skate and carpet shark genera. Moving forward we would expect to find additional members of this group parasitizing other species of parascyliid carpet sharks as well as other species of the rajid genus Malacoraja and the arhynchobatid genus Brochiraja. Here we have doubled the number of described species in the taxon referred to as Clade 1 while simultaneously expanding our understanding of the morphology and anatomy of its members. This additional information will help inform the ultimate revision of the ordinal classification of the cestodes to address the highly polyphyletic nature of the order "Tetraphyllidea" as it is currently configured.