Senate Republicans are circulating an updated version of their latest proposal to overhaul the 2010 health care law. The new draft bill was obtained by CQ Roll Call.

The updated bill, from Sens. Lindsey Graham, R-.S.C., and Bill Cassidy, R-La., would overhaul the 2010 health care law. It appears to seek to address concerns of senators who haven’t supported the plan.

The Department of Health and Human Services claimed Alaska, Arizona, Kentucky and Maine would all see increases in funding under the plan compared to current law, according to a state-by-state analysis circulating around Capitol Hill.

Support from senators from at least two of those states is necessary for Republicans to pass a bill before a key Sept. 30 deadline for rolling back the law with a simple majority of 51 votes. The state-by-state analysis, however, doesn’t account for the per-beneficiary cap on federal Medicaid funding which would cause states to lose funding under the bill.

Alaska and Kentucky actually would see a reduction in federal funding. The HHS chart suggests that the states would save from not paying its current share of funds to cover Medicaid expansion beneficiaries, since Medicaid expansion would be repealed under the bill.

Sen. John McCain, R-Ariz., has said he won’t vote for the proposal based on the process. Sen. Rand Paul, R-Ky., warned in an interview with The Washington Post on Sunday that any changes to win him over would likely alienate more moderate Republicans.

Sen. Lisa Murkowski, R-Alaska, hasn’t said how she would vote for the plan but is seen as a key vote, given her previous opposition to other repeal legislation. Sen. Susan Collins, R-Maine, said Sunday it was difficult to see a situation in which she would vote for it.

The updated bill also seeks to put pressure on states to more clearly state how they would keep insurance coverage “adequate and affordable” for individuals with pre-existing conditions, which has been a criticism of the earlier draft. The new language says a state “shall” describe how it would maintain access to “adequate and affordable” coverage for sick patients as part of an application for a state to receive a block grant.

But under the proposal, states would be able to design insurance regulations on issues including how much more insurers could charge older people than young people, required health benefits and whether to allow multiple risk pools, among other things. That could appease conservative Republicans such as Sen. Ted Cruz, R-Texas, who said earlier Sunday he didn’t support the previous version of the bill.

Under the new draft, states would still receive block grants help finance health insurance, as opposed to current funding for tax credits, cost-sharing reduction payments and Medicaid expansion. The latest draft would also transition Medicaid to a per capita based system, instead of its current open entitlement program.

Minority Leader Charles E. Schumer of New York criticized the new plan.

“Despite an attempt to appear to add money for a select few states, this bill is just as bad for those states and the rest of the states because it still contains a massive cut to Medicaid, and would throw our health insurance system into chaos while raising premiums,” Schumer said Sunday night. “It still takes away protections for those with preexisting conditions and further weakens consumer protections. Rather than making haphazard, last-minute changes to a partisan bill that won’t be scored by the [Congressional Budget Office] in time for a vote, we should resume the bipartisan negotiations between Senators [Patty Murray, D-Wash., and Lamar Alexander, R-Tenn.]”