Complex gene regulatory mechanisms underlie differentiation and reprogramming. Contemporary single-cell lineage-tracing (scLT) methods use expressed, heritable DNA barcodes to combine cell lineage readout with single-cell transcriptomics. However, reliance on transcriptional profiling limits adaptation to other single-cell assays. With CellTag-multi, we present an approach that enables direct capture of heritable random barcodes expressed as polyadenylated transcripts, in both single-cell RNA sequencing and single-cell Assay for Transposase Accessible Chromatin using sequencing assays, allowing for independent clonal tracking of transcriptional and epigenomic cell states. We validate CellTag-multi to characterize progenitor cell lineage priming during mouse hematopoiesis. Additionally, in direct reprogramming of fibroblasts to endoderm progenitors, we identify core regulatory programs underlying on-target and off-target fates. Furthermore, we reveal the transcription factor Zfp281 as a regulator of reprogramming outcome, biasing cells toward an off-target mesenchymal fate. Our results establish CellTag-multi as a lineage-tracing method compatible with multiple single-cell modalities and demonstrate its utility in revealing fate-specifying gene regulatory changes across diverse paradigms of differentiation and reprogramming.