Pennsylvania Gov. Tom Corbett (R) rejected the expansion in February but is reportedly planning to speak with federal Health and Human Services Secretary Kathleen Sebelius on April 2 about a compromise deal.
Arkansas, Ohio and Tennessee are also seeking alternative ways to go about the Medicaid expansion.
So far, eight Republican and 17 Democratic governors have agreed to pursue the policy, often under pressure from hospitals coping with uncompensated care.
RAND reported Thursday that uncompensated care in Pennsylvania cost hospitals $990 million in 2011.
The Medicaid expansion, along with other provisions of the Affordable Care Act, would lower Pennsylvania's share of uninsured residents to 5 percent, RAND said.
—This post was changed Friday at 1:13 p.m. to reflect that 340,000 Pennsylvanians, not 240,000, would gain coverage under the expansion per RAND's study.