This paper is concerned with a line of research which has recently attracted much attention, causal discovery from data with soft interventions with unknown targets. The paper extends previous results and proposes an improve scheme to solve the problem. The paper is nice written, with completeness results of the proposed scheme. Its arguments for using pairwise comparison of the distributions are clear and sensible. Reviewers feel positive about the paper and it is worth accepting; at the same time, they feel that the paper would be stronger if a comparison against independent change-based causal discovery methods, e.g., CD-NOD ( and subsequent publications), were given. As illustrated in the paper (supplementary material), if one uses invariance for causal discovery from multiple distributions, then pairwise comparison may be superior to the joint comparison scheme. This 'non-monotonicity' property of invariance also suggests that the condition of invariance may be restrictive. In fact, it is a particular case of the independence change principle --a constant is independent from everything. With independent change principle, one can directly benefit from more domains/distributions. Reviewers are aware of the fact that this paper adopts the FCI framework while CD-NOD uses the PC framework; nevertheless, the authors may want to consider providing a theoretical comparison and/or empirical comparisons on systems with or without confounders.