I was working with a WPP executive on telling a more effective story for a new client with whose industry she wasn't entirely familiar. She called me because the old tricks just weren't working for her.
Persuasion often involves what my friend James calls English-to-English translation: the ability to take language that one person believes describes the world and apply it to your argument about the world that might be quite different.
Natural language --eg replacing jargon with words we use everyday -- is generally more effective than replacing one set of industry terms for another. See TED for ways in which very clever people make very complex issues entirely straightforward entirely by translating language usually reserved for specialists into layperson's terms.
You don't have to go back to Plato to argue that every argument is an interpretation -- it's credibility that separates a business case from a rationalisation. So be familiar with every convention within the context you're pitching -- convention is, by definition, what people take for granted. Then you can build your argument in a way that will sell.