Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitaev, and Zhang established the shape-Wilf-equivalence for individual claw-shaped POPs. In this paper, we extend their result by proving that certain families of claw-shaped POPs are shape-Wilf-equivalent and enumerate the number of permutations avoiding that set of claw-shaped POPs. Our approach is based on a new encoding process, which is entirely different from the method used in their work.