We introduce the sequential multi-object robotic grasp sampling algorithm SeqGrasp that can robustly synthesize stable grasps on diverse objects using the robotic hand’s partial Degrees of Freedom (DoF). We use SeqGrasp to construct the large-scale Allegro Hand sequential grasping dataset SeqDataset and use it for training the diffusion-based sequential grasp generator SeqDiffuser. We experimentally evaluate SeqGrasp and SeqDiffuser against the state-of-the-art non-sequential multi-object grasp generation method MultiGrasp in simulation and on a real robot. The experimental results demonstrate that SeqGrasp and SeqDiffuser reach an 8.71%-43.33% higher grasp success rate than MultiGrasp. Furthermore, SeqDiffuser is approximately 1000 times faster at generating grasps than SeqGrasp and MultiGrasp. Project page: https://yulihn.github.io/SeqGrasp/.