The deadly shooting at Washington D.C.’s Navy Yard is promoting Senators to consider a fresh attempt to advance legislation strengthening background checks for gun buyers, Bloomberg reports.

Senate Majority Leader Harry Reid says he’ll schedule another vote to expand firearms background checks “as quickly as we can” when enough members support the bill. He spoke a day after government contractor Aaron Alexis opened fire inside the Navy Yard complex about a mile from the U.S. Capitol, killing 12 people before being shot himself by the police.

The senators in favor of the background-check legislation that failed following the Sandy Hook shooting expressed optimism that they may be able to gather additional votes by combining a measure dealing with mental health issues with the previous bill.