Droplet-based single-cell RNA-seq (dscRNA-seq) data are being generated at an unprecedented pace, and the accurate estimation of gene-level abundances for each cell is a crucial first step in most dscRNA-seq analyses. When pre-processing the raw dscRNA-seq data to generate a count matrix, care must be taken to account for the potentially large number of multi-mapping locations per read. The sparsity of dscRNA-seq data, and the strong 3' sampling bias, makes it difficult to disambiguate cases where there is no uniquely mapping read to any of the candidate target genes. We introduce a Bayesian framework for information sharing across cells within a sample, or across multiple modalities of data using the same sample, to improve gene quantification estimates for dscRNA-seq data. We use an anchor-based approach to connect cells with similar gene-expression patterns, and learn informative, empirical priors which we provide to alevin's gene multi-mapping resolution algorithm. This improves the quantification estimates for genes with no uniquely mapping reads (i.e. when there is no unique intra-cellular information). We show our new model improves the per cell gene-level estimates and provides a principled framework for information sharing across multiple modalities. We test our method on a combination of simulated and real datasets under various setups. The information sharing model is included in alevin and is implemented in C++14. It is available as open-source software, under GPL v3, at https://github.com/COMBINE-lab/salmon as of version 1.1.0.