One specific effort was Prohibition.  Prohibition did not pass during the time period you specify, but efforts toward it were ongoing.  The Progressives wanted to reform immigrants and get them to stop drinking so much so they could be more like middle class Americans.

Another effort was the one to get direct election of Senators.  This was done to decrease levels of corruption in government.  The Progressives wanted to stop the rich from "buying" government officials.

Finally, there were the efforts to create referendums, recall elections, and initiatives.  These were meant to create more direct democracy.  The idea was that this would reduce the power of corrupt legislatures and give more power to the people.