Cheap open-ended ticket to South America?

You need a one way ticket. I’ve heard you get hassled by TSA at airports now if you have a one way. There’s not much you can do about the price if you go this route. Just plan ahead a bit so you don’t have to buy the ticket at an airport counter. Another option is to buy a roundtrip or multi-city fare and either stick with this pre-arranged plan or pay the change fee later. There used to be this thing called vouchers where I live where you could buy a ticket in advance and use it anytime within a certain period of time like a year. I think this no longer exists, but might be worth inquiring about. A round trip ticket may sound like a ball and chain, but it is probably the cheapest way about it, and you could plan to make a loop so you don’t cross the same path twice.

I am going to assume you already checked into round trip tickets that are open ended or have no change or cancellation fee. They are usually expensive, but so are one way tickets usually. Also sometimes it is simply cheaper to buy a round trip and not use the return.

Maybe contact a travel agent in Argentina and one of the other countries you plan to go to. One of the airlines in South America might have some sort of deal. So, for instance if you will be going to Colombia, Avianca might have a decent price from Buena Aires to Bogota and then on to America at a later date. Booking a ticket like that is probably cheaper than booking a one way for each hop to a new country as one way tickets.

Also, I would call American Airlines, they services the Americas more than an other American airline from what I can tell.

I don’t think flying on a one way ticket will give you much trouble in security if you don’t have any other red flags. People vacation for months at a time, and I doubt they all buy round trips.