Real-world sparse matrices often feature multiple forms of structured sparsity, e.g., dense rectangular blocks, diagonal bands, and scattered entries. Hybrid storage formats can exploit such structure by storing each subregion of a ma- trix in its most efficient form. Existing hybrid approaches, however, only support fixed sets of formats and kernels, so incorporating a new representation or kernel requires modifying their internals. We present SABLE, a framework that lets users build bespoke hybrid formats compositionally through a plan–extract–dispatch interface. Users define extractors that carve a matrix into format-specific regions and kernels that emit specialized C code for each region; SABLE assembles these pieces into a single program specialized to the target matrix at compile time. Both components are independent and composable, so a new format automatically integrates with all existing kernels without any changes to the framework. We demonstrate this extensibility by introducing VDIA, a new format for diagonal bands of non-uniform length, and composing it to build two new hybrid formats—VDIA+CSR and VDIA+VBR+CSR. We evaluate SABLE on SpMV and SpMM over SuiteSparse matrices whose structure comprises dense blocks, diagonal bands, or both, demonstrating geometric-mean speedups over the best fully-sparse baselines of 1.10 × /1.20× (SpMV/SpMM) for blocks and 1.14 × /1.31× for bands; composing all three formats yields a further 1.12 × /1.17× speedup