Background: Total-RNA sequencing (total-RNA-seq) allows the simultaneous study of both the coding and the non-coding transcriptome. Yet, computational pipelines have traditionally focused on particular biotypes, making assumptions that are not fullfilled by total-RNA-seq datasets. Transcripts from distinct RNA biotypes vary in length, biogenesis, and function, can overlap in a genomic region, and may be present in the genome with a high copy number. Consequently, reads from total-RNA-seq libraries may cause ambiguous genomic alignments, demanding for flexible quantification approaches. Results: Here we present Multi-Graph count (MGcount), a total-RNA-seq quantification tool combining two strategies for handling ambiguous alignments. First, MGcount assigns reads hierarchically to small-RNA and long-RNA features to account for length disparity when transcripts overlap in the same genomic position. Next, MGcount aggregates RNA products with similar sequences where reads systematically multi-map using a graph-based approach. MGcount outputs a transcriptomic count matrix compatible with RNA-sequencing downstream analysis pipelines, with both bulk and single-cell resolution, and the graphs that model repeated transcript structures for different biotypes. The software can be used as a python module or as a single-file executable program. Conclusions: MGcount is a flexible total-RNA-seq quantification tool that successfully integrates reads that align to multiple genomic locations or that overlap with multiple gene features. Its approach is suitable for the simultaneous estimation of protein-coding, long non-coding and small non-coding transcript concentration, in both precursor and processed forms. Both source code and compiled software are available at https://github.com/hitaandrea/MGcount.