title_body: A Hypothetical Mediterranean Language Inspired by Both Greek and Latin
upvoted_answer: The situation you describe, in which Classical Greece invades the Roman Republic, has two probable outcomes. (This is assuming a single language "merged into one" excludes the possibility of both languages coexisting. However, a language can also exert influence on another without supplanting it.)
  
  
  If the Romans adopted (or were forced to adopt) their conquerors' language, which is what happened in other nations after Alexander the Great's conquests later in history, then the spoken language would become Greek. The influence of the Latin language in such a case would exist as a substrate, which could introduce Latin loan words and grammatical structures into Roman Greek.
  If the Romans didn't choose (or weren't forced) to adopt Greek as their language and continued to speak Latin, then Latin would remain the spoken language, but would have Greek influence on vocabulary and grammar, as a superstrate or adstrate. As it is, Latin already has Greek influence on its vocabulary, with learned words like philosophia; but in the case of a Greek conquest, it would probably gain more mundane words as well.
  
  
  A comparable case in history with regard to English could be the Norman invasion of England. Anglo-Norman and English were spoken alongside each other. Eventually, English was the only language spoken of the two in England, but not without considerable influence from Anglo-Norman. Looking at this case might give an idea of how a language could change followed by the invasion of another one.