It can't be done, and it wouldn't make it faster, assuming you are setting your limits correctly.
Both clients would theoretically be trying to connect to the same pool of seeders and leechers. Each client would randomly have a chance of getting better seeders and leechers, but assuming that there are enough of each, you will be maxing out your download bandwidth anyways.
The only potential advantage you might get from running 2 clients (if this were possible) is would have more connections per torrent, but this is generally configurable in each client anyways, and is usually set to a reasonable default. So I don't think it would really provide any benefit.
As you mentioned, one client would have to know which piece the other is downloading, otherwise there would be a massive duplication of work.
If you found two clients that didn't explode immediately when you tried this, you would likely have issues with both clients trying to write to the file at the same time, you would have many duplicate blocks downloaded and in the end your download would take far longer than it should have.