We investigate the potential of graph neural networks (GNNs) for transfer learning and improved molecular property prediction in the context of funnels or screening cascades characteristic of drug discovery and/or molecular design. GNNs have emerged as a powerful and widely used class of algorithms for molecular property prediction thanks to their natural ability to learn from molecular structures represented as atoms and bonds , as well as in the life sciences in general . However, their potential for transfer learning is yet to be established. The screening cascade refers to a multi-stage approach where one starts with cheap and relatively noisy methods (high-throughput screening, molecular mechanics calculations, etc.) that allow for screening a large number of molecules. This is followed by increasingly accurate and more expensive evaluations that come with much lower throughput, up to the experimental characterisation of compounds. Individual stages or tiers in the screening funnel are, thus, used to make a reduction of the search space and focus the evaluation of more expensive properties on the promising regions. In this way, the funnel maintains a careful trade-off between the scale, cost, and accuracy. The progression from one tier to another is typically done manually by selecting subsets of molecules from the library screened at the previous stage or via a surrogate model that focuses the screening budget of the next step on the part of the chemical space around the potential hits. Such surrogate models are typically built using the data originating from a single tier and, thus, without leveraging measurements of different fidelity.