Spherical deconvolution is a widely used approach to quantify the fiber orientation distribution (FOD) from diffusion MRI data of the brain. The damped Richardson-Lucy (dRL) is an algorithm developed to perform robust spherical deconvolution on single-shell diffusion MRI data while suppressing spurious FOD peaks due to noise or partial volume effects. Due to recent progress in acquisition hardware and scanning protocols, it is becoming increasingly common to acquire multi-shell diffusion MRI data, which allows for the modelling of multiple tissue types beyond white matter. While the dRL algorithm could, in theory, be directly applied to multi-shell data, it is not optimised to exploit its information content to model the signal from multiple tissue types. In this work, we introduce a new framework based on dRL – dubbed generalized Richardson-Lucy (GRL) – that uses multi-shell data in combination with user-chosen tissue models to disentangle partial volume effects and increase the accuracy in FOD estimation. Further, GRL estimates signal fraction maps associated to each user-selected model, which can be used during fiber tractography to dissect and terminate the tracking without need for additional structural data. The optimal weighting of multi-shell data in the fit and the robustness to noise and to partial volume effects of GRL was studied with synthetic data. Subsequently, we investigated the performance of GRL in comparison to dRL and to multi-shell constrained spherical deconvolution (MSCSD) on a high-resolution diffusion MRI dataset from the Human Connectome Project and on an MRI dataset acquired at 3T on a clinical scanner. In line with previous studies, we described the signal of the cerebrospinal-fluid and of the grey matter with isotropic diffusion models, whereas four diffusion models were considered to describe the white matter. With a third dataset including small diffusion weightings, we studied the feasibility of including intra-voxel incoherent motion effects due to blood pseudo-diffusion in the modelling. Further, the reliability of GRL was demonstrated with a test-retest scan of a subject acquired at 3T. Results of simulations show that GRL can robustly disentangle different tissue types at SNR above 20 with respect to the non-weighted image, and that it improves the angular accuracy of the FOD estimation as compared to dRL. On real data, GRL provides signal fraction maps that are physiologically plausible and consistent with those obtained with MSCSD, with correlation coefficients between the two methods up to 0.96. When considering IVIM effects, a high blood pseudo-diffusion fraction is observed in the medial temporal lobe and in the sagittal sinus. In comparison to dRL and MSCSD, GRL provided sharper FODs and less spurious peaks in presence of partial volume effects, but the FOD reconstructions are also highly dependent on the chosen modelling of white matter. When performing fiber tractography, GRL allows to terminate fiber tractography using the signal fraction maps, which results in a better tract termination at the grey-white matter interface or at the outer cortical surface. In terms of inter-scan reliability, GRL performed similarly to or better than compared methods. In conclusion, GRL offers a new modular and flexible framework to perform spherical deconvolution of multi-shell data.