Answer is yes, by a logical approach, in superior organism where alternative splicing and post-transcriptional modification alter the protein structure.
In bacteria, this thing is not allowed. This scenario isn't common in functional protein, and start occurring by some alteration in the splicing process.
In real life, this is nearly impossible. A protein domain could be conserved, and so different protein can share parts of the amminoacidic sequence and, by that, the mRNA. But, as far as I know, there's no study confirming the evidence of same transcript and different proteins.