In this work, we investigated multi-fidelity learning approaches with GNN models for predicting toluene/water partition coefficients for which experimental data are only readily available in the order of a few hundred values. First, we used COSMO-RS to create a low fidelity dataset of partition coefficients for about 9,000 molecules. The low fidelity data in combination with the available high fidelity experimental data was then utilized for training GNN models. Our results showed that multi-target learning, i.e., predicting low fidelity and high fidelity target properties with one GNN model, yields substantial accuracy increases to training a GNN model on the experimental data only and is superior to transfer learning and feature-augmented learning. We further found competitive accuracy of the multi-target GNN model compared to other predictive models, e.g., based on activity coefficients and solvation free energies, and other methods such as COSMO-RS. Overall, the comparison of the different approaches for partition coefficient predictions shows that direct training on log P data is most effective. Here, multi-fidelity learning in the form of multi-target learning substantially increases the predictive accuracy. This is particularly interesting as the multi-target learning approach presumably requires the least training and model changes, i.e., just an additional model output, and is thus straightforward to implement. Generating additional molecular property data through QC calculations for training predictive ML models like GNN models is thus highly promising to enhance the predictive quality when available experimental data is limited, such as for toluene/water partition coefficients. However, it is important to acknowledge that the availability of high fidelity data remains a significant challenge and the extrapolation to new chemical classes cannot be fully resolved with multi-fidelity learning approaches leveraging large low fidelity datasets.