We present modelings of high-order line singularities encoded in space-variant polarization of light. This involves calculating the line patterns produced by the superposition of light beams in orthogonal states of circular polarization, with each beam carrying an optical vortex, and where one of them is asymmetric. This setting allowed us to study the case of monstars of high order. We find that monstars can have positive or negative singularity indices, modifying the previous understanding of the pattern, which was based on the case of lowest-order C- points. Monstars then remain characterized only by their own unique feature: sectors with patterns of mostly curved lines that radiate from the center. Given this definition, we propose that the case where the index is +1 be classified as a monstar. We also found that the asymmetric modes contain kinks that appear in the C-lines of a distinct but related pattern that contains line orientation discontinuities.