Nanoparticle-based clusters permit the harvesting of collective and emergent properties, with applications ranging from optics and sensing to information processing and catalysis. However, existing approaches to create such architectures are typically system-specific, which limits designability and fabrication. Our work addresses this challenge by demonstrating that cluster architectures can be rationally formed using components with programmable valence. We realize cluster assemblies by employing a three-dimensional (3D) DNA meshframe with high spatial symmetry as a site-programmable scaffold, which can be prescribed with desired valence modes and affinity types. Thus, this meshframe serves as a versatile platform for coordination of nanoparticles into desired cluster architectures. Using the same underlying frame, we show the realization of a variety of preprogrammed designed valence modes, which allows for assembling 3D clusters with complex architectures. The structures of assembled 3D clusters are verified by electron microcopy imaging, cryo-EM tomography and in-situ X-ray scattering methods. We also find a close agreement between structural and optical properties of designed chiral architectures.