Sintering is a physically complex process that includes various mechanisms interacting and competing with each other. The phase-field method is perceived by the community as one of the most optimal tool for modeling of sintering as it is able to plausibly capture all relevant physical phenomena: mass transport, grain growth, and mechanical interactions of particles. Despite attractiveness and proven versatility, the phase-field based models posses a significant drawback - high computational costs. On average 10,000 scalar degrees of freedom are required per particle to accurately capture the interface dynamics in 3D. With the need to have at least 1,000 particles in a representative volume element in order for the numerical results to be deemed as statistically relevant, this leads to at least 10,000,000 of scalar degrees of freedom in total. This fact, together with the complexity of the underlying physics, poses severe requirements on the efficiency of the numerical implementation in order to successfully handle such large and challenging systems. We present hpsint, an efficient solver for the simulation of many-particle solid-state-sintering processes. The microstructure evolution is described by a system of one Cahn-Hilliard (CH) and a set of Allen-Cahn (AC) equations to distinguish neighboring particles. In order to keep the number of AC equations minimal, we reuse the same AC equation for multiple particles tracking the topology of the microstructure such that potential collisions of particles belonging to the same AC is avoided. This is achieved by a novel fully distributed graph based grain-tracking algorithm. The developed solver also includes the adaptive mesh refinement strategy, the efficient evaluation of the Jacobian matrix as well as the implementation of Jacobian-free methods by applying state-of-the-art matrix-free algorithms for high and dynamic numbers of components, and advances in block preconditioning. We examine in detail the node-level performance and demonstrate the scalability up to 10,000 particles on modern supercomputers. Our framework thus forms a valuable tool for the virtual design of solid-state-sintering processes for pure metals and their alloys. Thanks to the modular well structured design, the framework can be successfully used for phase-field problems of other types.