Sparse matrix–vector multiplication (SpMV) is a fundamental kernel in many applications, yet its performance is severely limited by irregular memory accesses and the accumulation of partial results on conventional architectures. While processing-in-memory (PIM) architectures mitigate data-movement overhead using high internal bandwidth, efficiently handling sparse data layouts and reducing partial results across distributed memory banks remain key challenges. This paper proposes SparsePIM+, an HBM-based PIM architecture that accelerates SpMV through software–hardware co-design. SparsePIM+ introduces a software optimization that clusters matrix columns based on row-index similarity while balancing non-zero element distribution across bank groups to improve accumulation parallelism. It also employs a DRAM row-aligned sparse format (DRAF) that aligns sparse operands with DRAM row-buffer granularity to reduce indirect memory accesses and redundant data movement. On the hardware side, SparsePIM+ integrates bank-group accumulators (BGAs) for local accumulation within each bank group, where a bank group consists of four banks, and a logic-die global accumulator (GA) that aggregates partial results across bank groups via a lightweight arbitrator. The accumulated results are stored in an on-die buffer accessible by host memory controllers, enabling concurrent PIM execution and accumulation. Experimental results show that SparsePIM+ significantly improves accumulation efficiency and achieves an average speedup of 1.38x over prior HBM-based PIM designs for SpMV and 6.16x over an NVIDIA RTX 3080 GPU baseline, with a maximum speedup of up to 15.48x.