What are some examples of genes that code for multiple proteins?
There are a large number of ways a protein variant can be produced by post translational modification.  The question may seem obvious, but its really quite broad. 

I can start this out.  I doubt I know all the ways a single transcript can produce variant proteins.   A detailed description might be more like a review article than an answer here. 

First, there are very rare cases of eukaryotic polycistronic mRNA: mRNA which code for more than one protein.  In this case, after translation, the mRNA are processed to make multiple monocistronic RNA.

Then there are proteins with molecules added by covalent bonding to the protein.  Glycoproteins are notoriously variable. Many other small molecules can be bonded to a protein to make a variant of this sort: ubiquitinization, N-acetylation, SUMO domains, lysine methylation are just a few of the more common covalent modifications of proteins. 

There are RNA editing which removes some of the coding RNA to make alternative splice RNA.  

The list goes on and on. So does any of this come close to what you wanted to know?