Metal-Organic Frameworks can be grafted with amines by coordination to metal vacancies to create amine-appended solid adsorbents, which are being considered as an alternative to using aqueous amine solutions for CO₂ capture. In this study, we propose an alternative mechanism that does not rely on the use of neutral metal vacancies as binding sites but is enabled by the structural adaptability of heterobimetallic Ti₂Ca₂ clusters. The combination of hard (Ti⁴⁺) and soft (Ca²⁺) metal centers in the inorganic nodes of the framework enables MUV-10 to adapt its pore windows to the presence of triethylenetetramine molecules. This dynamic cluster response facilitates the translocation and binding of tetraamine inside the microporous cavities to enable the formation of bis-coordinate adducts that are stable in water. The extension of this grafting concept from MUV-10 to larger cavities not restrictive to CO₂ diffusion will complement other strategies available for the design of molecular sorbents for decarbonization applications.