Branching fractions and CP-violating asymmetries of charmless B¯s0→PPP decays with P=K, π are studied using a simple model based on the factorization approach. The penguin-dominated modes B¯s0→K¯0K+π- and K0K-π+ have the largest rates among the three-body Bs decays, and they are dominated by the K0*(1430) resonances and nonresonant contributions. The branching fraction of B¯s0→K0K+K- is predicted to be of order 1.4×10-6, which is in the middle of the measured result (0.2–3.4)×10-6 obtained by LHCb. We find sizable CP violation in K0π+π-, K0π0π0, K0K+K-, and KSKSKS channels. Just as the Bu sector, the CP asymmetries of B¯s0→K0π+π- and B¯s0→K0K+K- have similar magnitudes but are opposite in sign. Several model-independent relations based on U-spin symmetry for CP asymmetries are derived. Although they cannot be tested by the present available data, they can be checked by the dynamical calculations. Since the U-spin symmetry that relates various matrix elements of scalar densities, for example, ⟨K0K|d¯q|0⟩ and ⟨K¯0π|s¯q|0⟩, is badly broken, the derived U-spin relations are generally not well respected.