No, you need a visa each for each of the countries you plan to visit in South America.
http://en.wikipedia....banese_citizens
I am assuming you have a Lebanese passport, which I am sorry to say considered a Tier 4 passport on a scale of 1 to 5 with 1 being the best. You could travel to Ecuador without a visa and get a visa on arrival in Bolivia. For rest of the countries, you need a visa. Usually when one of the South American countries issue a visa, rest of the neighboring countries give you a visa more easily.
You could also try to be arrive just on Argentine visa. And then once here, try to get the other visas from respective embassies located in BA. However, their is a danger here, of being refused as they might tell you, "
please go and apply in your home country."
Hope this helps.