Diffusion magnetic resonance imaging (dMRI) provides insight into the micro and macro-structure of the brain. Multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD) models the underlying local fiber orientation distributions (FODs) using the dMRI signal. While generally producing high-quality FODs, MSMT-CSD is a voxel-wise method that can be impacted by noise and produce erroneous FODs. Local models also do not use the spatial correlation between neighboring voxels to increase parameter estimating power. Additionally, voxel-wise methods require interpolation at arbitrary locations outside of voxel centers. These interpolations can be computationally costly or inaccurate, depending on the method of choice. Expanding upon previous work, we apply the implicit neural representation (INR) methodology to the MSMT-CSD model. This results in an unsupervised machine-learning framework that generates a continuous representation of a given dMRI dataset. The input of the INR consists of coordinates in the volume, which produce the spherical harmonics coefficients parameterizing an FOD at any desired location. A key characteristic of our model is its ability to leverage spatial correlations in the volume, which acts as a form of regularization. We evaluate the output FODs quantitatively and qualitatively in synthetic and real dMRI datasets and compare them to existing methods.