Housing benefit, along with attendance allowance paid to over 65s with disabilities for help with personal care, would be devolved to Holyrood under proposals put forward by Scottish Labour.
The work programme, under which organisations are paid to help unemployed people into work, would also be devolved.
The announcement comes as campaigners for and against independence mark six months until Scotland's referendum.
We believe our proposals set out the most comprehensive package of devolution.
It also said that MSPs would be able to vary tax by up to 15p with the option of restoring the 50p rate for top earners.
While most other benefits would remain reserved by the Westminster government, gaining control of attendance allowance and housing benefit would enable Scotland to redress some of the bigger social injustices according to Labour, not least the controversial bedroom tax.
Scottish Labour leader Johann Lamont said: "The commission has worked hard to ensure that our proposals are consistent with Scotland remaining strong in the United Kingdom but also give us the flexibility to do things differently where we want to.
"We believe our proposals set out the most comprehensive package of devolution while also allowing Scotland the security and certainty of the United Kingdom."
The Scottish Conservatives has set up its own commission to look at further powers for the Scottish Parliament while the Liberal Democrats has published a report arguing for Scotland to raise and spend most of its own taxes.