In order for this to happen Rome would need to avert the invasions it suffered before it ultimately fell. Then if it could it then could expand into Germany and then onward to Scandinavia and Eastern Europe and perhaps all the way to the Ural Mountains after technology advanced. Perhaps Rome could have adopted weapons like crossbows, mongol bows and later firearms. Then the Roman Empire could have colonized North and South America entirely. Historically the americas were primarily colonized by Spain, Portugal, England (and later Britain), France and Russia. If there is still an industrial revolution and a period of modernization then Rome may have become a truly powerful empire with a large economy and powerful military. Perhaps when the Mughal empire collapsed then the Roman Empire could have colonized India. As for Siberia the Roman Empire may have conquered and colonized that area as well. Without America to open Japan up then Japan could have stayed backwards only to be conquered by the Roman Empire. If China ever had a warlord era in this scenario then China may have been conquered by Rome too. If the Roman Empire survived then maybe the earth may be under roman domination and the Roman Empire would be a superpower and possibly a hyperpower. Latin would be a lingua Franca. Latin-speaking men may have been the first men in space and on the moon. Maybe Rome may have annexed most of the planets of the solar system too. What do you think would have happened if the Roman Empire survived?