I sell software and the software company gives me a 1099. Can I get other salespeople to sell the software, pay them a portion of what I get paid, and give them a 1099? I am not a business.

Actually yes you are a business, that is basically what a 1099 worker is, You are a independent contractor who has their own business and sells a company product. In return they pay you for that.

So yes, in fact if you are paying them, you are are required to give a 1099 if it is over a certain amount. ( used to be 400 dollars a year, but I have not keep up with the current amount)