Heterogeneous accelerator-rich (ACC-rich) platforms combining general-purpose cores and specialized HW accelerators (ACCs) promise high-performance and low-power streaming application deployments in a variety of domains, such as video analytics and software-defined radio. In order to benefit a domain of applications, a domain platform exploration tool must take advantage of structural and functional similarities across applications by allocating a common set of ACCs. A previous approach proposed a genetic domain exploration tool (GIDE) that applied a restrictive binding algorithm that mapped applications functions to monolithic accelerators. This approach suffered from a low average application throughput across and reduced platform generality. This article introduces a multigranularity-based domain design space exploration tool (MG-DmDSE) to improve both average application throughput as well as platform generality. The key contributions of MG-DmDSE are: 1) applying a multigranular decomposition of coarse-grained application functions into more granular compute kernels; 2) examining compute similarity between functions in order to provide more generic functions; 3) configuring monolithic ACCs by selectively bypassing compute elements within them during DSE to expose more functionality; and 4) speeding up MG-DmDSE platform allocation exploration through a greedy guided mutation (GGM) algorithm. To assess MG-DmDSE, both GIDE and MG-DmDSE were applied to applications in the OpenVX library. MG-DmDSE achieves an average <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.84\times $ </tex-math></inline-formula> greater application throughput compared to GIDE. Additionally, 87.5% of applications benefited from running on the platform produced by MG-DmDSE versus 50% from GIDE, which indicated increased platform generality. The generated MG-DmDSE platforms achieve an average of 61.8% logarithmic throughput improvement for unknown applications over GIDE. GGM results in saving 84.8% of the exploration time in MG-DmDSE with only 0.23% performance loss.