Clustering　is　one　of　the　most　fundamental　tools　in　artificial　intelligence,　machine　learning,　and　data　mining.　In　this　paper,　we　follow　one　of　the　recent　mainstream　topics　of　clustering,　Sum　of　Radii　(SoR),　which　naturally　arises　as　a　balance　between　the　folklore　k-center　and　k-median.　SoR　aims　to　determine　a　set　of　k　balls,　each　centered　at　a　point　in　a　given　dataset,　such　that　their　union　covers　the　entire　dataset　while　minimizing　the　sum　of　radii　of　the　k　balls.　We　propose　a　general　technical　framework　to　overcome　the　challenge　posed　by　varying　radii　in　SoR,　which　yields　fixed-parameter　tractable　(fpt)　algorithms　with　respect　to　k　(i.e.,　whose　running　time　is　f(k)ploy(n)　for　some　f).　Our　framework　is　versatile　and　obtains　fpt　approximation　algorithms　with　constant　approximation　ratios　for　SoR　as　well　as　its　variants　in　general　metrics,　such　as　Fair　SoR　and　Matroid　SoR,　which　significantly　improve　the　previous　results.　Copyright　©　2024,　Association　for　the　Advancement　of　Artificial　Intelligence　(www.aaai.org).　All　rights　reserved.