Many genes are arranged in complex overlapping and interlaced patterns in eukaryotic genomes. It is unclear whether or how such genes can avoid interference from each other's RNA processing signals and retain distinct identities. This puzzle applies particularly to 3' end formation sites, which inherently terminate the transcript, and thus act as boundaries between adjacent genes. We hypothesise that the transcript processing machinery can bypass 3' end formation sites by splicing out an intron surrounding the site. We confirm a prediction of this hypothesis: the likelihood of transcripts extending beyond 3' end sites depends on the strength of 3' end formation signals located in exons in the mature transcript, but not of those in introns that are spliced out of the transcript. This bypassing mechanism permits nested and interleaved gene architectures, as well as fusion transcripts that combine exons from adjacent genes.