The Senate on Thursday advanced a bill known as the Laken Riley Act that is aimed at expanding the federal government’s mandate to detain immigrants who are in the country illegally.

In a 84 to 9 vote, the Senate voted to advance the legislation, with 31 Democrats joining all voting Republicans to clear a 60-vote threshold to begin debate. The bill marks the first policy legislation of the new Congress, and the House approved it in a bipartisan vote of its own on Tuesday.

Senate Majority Leader John Thune will now decide which, if any, amendments will be considered on the floor. Some Democrats who voted to proceed said they did so in order to offer changes to the legislation before deciding how they would vote on final passage.

The bill is named after Laken Riley, a 22-year-old nursing student who was murdered by an undocumented Venezuelan immigrant last year. A judge convicted the man, Jose Ibarra, on murder and other charges related to Riley’s death in November.