I don't believe that's possible with any mobile technology.
No, an App doesn't have access to the phone app.
But what you are describing, isn't it just 3 way calling? You start a convo with someone, add a person and then you hang up? Does that kill the entire call or do the others have the ability to stay connected?
Nevermind, just tested it, it ends all the calls if I disconnect.
Are you talking about a conference call?
No. The ability for person A to call me (person B) and for me (person B) to transfer person A to person C and for person B to hangup (so only A and B are talking)