MONTPELIER — Vermont’s Green Mountain Care Board is looking at what the effects might be on the state’s health care system if hospitals and other providers switch from nonprofit to for-profit status.

The board, which is designing the single-payer health care system the state is hoping to set up by 2017, has devoted a session set for Thursday afternoon to the subject of such conversions.

The issue comes up a year after Burlington-based Fletcher Allen Health Care sought — and then dropped the idea — to sell off its dialysis units to a for-profit New Hampshire company.

It also follows the announcement that Vermont’s hospitals and the Dartmouth-Hitchcock Medical Center in Lebanon, N.H., are joining to form a for-profit accountable care organization.