Universality of the $1\mathrm{/}9$ Magnetization Plateau and Quantum-Disordered States in the Kagome Family $\mathrm{C}{\mathrm{s}}_8\mathrm{A}{\mathrm{B}}_3\mathrm{T}{\mathrm{i}}_{12}{\mathrm{F}}_{48}$ ($A=\mathrm{R}\mathrm{b},\mathrm{L}\mathrm{i}$; $B=\mathrm{K},\mathrm{N}\mathrm{a}$)

The microscopic origin of the low-field $1\mathrm{/}9$ magnetization plateau in spin-$1\mathrm{/}2$ kagome antiferromagnets remains unresolved. Here, we show that chemical pressure reshapes the hierarchy of fractional magnetization plateaus in the titanium-based kagome family $\mathrm{C}{\mathrm{s}}_8\mathrm{A}{\mathrm{B}}_3\mathrm{T}{\mathrm{i}}_{12}{\mathrm{F}}_{48}$ ($A=\mathrm{R}\mathrm{b},\mathrm{L}\mathrm{i}$; $B=\mathrm{K},\mathrm{N}\mathrm{a}$). High-field magnetization measurements up to 60 T reveal a robust $1\mathrm{/}9$ plateau-like phase in the expanded $\mathrm{C}{\mathrm{s}}_8\mathrm{R}\mathrm{b}{\mathrm{K}}_3\mathrm{T}{\mathrm{i}}_{12}{\mathrm{F}}_{48}$ and $\mathrm{C}{\mathrm{s}}_8\mathrm{L}\mathrm{i}{\mathrm{K}}_3\mathrm{T}{\mathrm{i}}_{12}{\mathrm{F}}_{48}$ compounds, despite the absence of the conventionally more robust $1\mathrm{/}3$ plateau. In contrast, compressed $\mathrm{C}{\mathrm{s}}_8\mathrm{L}\mathrm{i}\mathrm{N}{\mathrm{a}}_3\mathrm{T}{\mathrm{i}}_{12}{\mathrm{F}}_{48}$ exhibits neither the $1\mathrm{/}9$ plateau-like phase nor a quantum-disordered ground state. Specific-heat measurements and first-principles calculations show that lattice expansion preserves a frustrated, fully connected kagome exchange network and gapless quantum-disordered ground states, whereas compression reorganizes the exchange network into weakly coupled quasi-one-dimensional subsystems and induces successive magnetic transitions. These results demonstrate that the $1\mathrm{/}9$ and $1\mathrm{/}3$ plateaus need not share a common microscopic origin and suggest that the $1\mathrm{/}9$ plateau may represent a more universal feature of frustrated spin-$1\mathrm{/}2$ kagome magnetism.