Sparse tensor algebra plays an important role in many scientific and engineering applications, yet existing sparse libraries and compilers face challenges when the output tensor is sparse. Array-based storage formats, such as CSR, require costly memory reallocations and rely on intermediate tensors (workspaces) to handle sparse scattering into the output, which limits performance and scalability. We introduce a new approach that employs our proposed flexible map-based storage format to directly support sparse scattering into the output without requiring extra workspaces. Our system then applies code and storage-specific optimizations. Experimental results across a range of kernels and datasets demonstrate an average speedup of $7.45\times$ over a state-of-the-art compiler and $5.29\times$ over a sparse tensor library.