As the Senate immigration bill moves toward a markup in the Judiciary Committee, Sen. Marco Rubio is signaling the changes he supports as he works to make the legislation more palatable to conservatives.

The Florida Republican is a key architect of the “gang of eight” proposal, and his continued backing is crucial to its prospects. A Rubio aide on Wednesday provided CQ Roll Call with a “sampling” of the kinds of amendments to the bill that the senator will urge the Judiciary Committee to approve. About 300 amendments have been filed in committee.

Changes Rubio would support include:

• An amendment mandating that specific portions of the southwest border be fenced with double-layered fencing, along with the funding to do it.

• Amendments that would strengthen the grounds for ineligibility/inadmissibility for currently undocumented aliens convicted of more than one misdemeanor.

• Amendments that would increase the number of background checks that immigrants are subject to as they go through the process to make sure they do not violate the criminal/national security grounds for eligibility. The issue has cropped up in the wake of the Boston Marathon bombing.

• Amendments that go after immigrants who commit welfare fraud, and by extension, those that create a rebuttable presumption that an immigrant is a public charge if they accept state and local welfare benefits.

• Amendments that eliminate all of the exceptions for eligibility for the Registered Provision Immigrant program for people who were illegally here and were either removed or left the country after Dec. 31, 2011 and then re-entered illegally. They should not be allowed to qualify for a program when they don’t meet the physical presence requirement that we fought for, Rubio contends.