"If more Independents joined the 2 major parties, and got them to expand their platforms and include more voices then the 2 party system would have broader appeal."

That used to be the way the Democratic party actually worked, until around the '80s. At that time, the party adopted a muscularly centrist policy and closed ranks. People who did not agree with their stance were strongly excluded.

There is no room in the Democratic party for anyone who is not OK with the policies of the Democratic Party establishment. That's why a lot of people left and became unaffiliated. The only way to have a real effect on the party is to have a pretty serious uprising.