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In this paper, we explore the relationship between the chamber decompositionfor K-semistable domains and VGIT. We also study the relationship between theK-moduli generically parametrizing K-semistable Fano complete intersections ofthe form $S_{d_1}\cap...\cap S_{d_k}$ and the K-moduli genericallyparametrizing K-semistable log Fano pairs of the form $(\mathbb{P}^n,\sum_{j=1}^kx_jS_{d_j})$, where $x_j\in (0,1)\cap \mathbb{Q}$ and$S_{d_j}\subset \mathbb{P}^n$ is a hypersurface of degree $d_j$ for each $1\leqj\leq k$.

Chamber decomposition for K-semistable domains and VGIT