Ottawa is asking the court for guidance on what it would take to reform the upper chamber, and whether it can abolish the body without provincial consultation.
Newfoundland and Labrador argues Ottawa alone cannot set term limits or have elections for senators, or outright abolish the upper chamber.
"The choices that are made about a national institution such as the Senate are fundamental choices about how Canadian society represents itself through sovereign government," the province says in its factum.
"They will have long-lasting effects on the way Canadian society is governed and on the operation of the federation. Any such changes should be the product of careful, thorough consideration and fulsome consultation between both constitutional orders of government, culminating in the achievement of the constitutionally required level of consensus."
Newfoundland and Labrador took no position on whether senators ought to own at least $4,000 worth of land in the province they represent, as the Constitution now requires.
Nunavut's deputy attorney general also argues that Parliament by itself lacks the authority to set Senate term limits, force elections or abolish the upper chamber. Like Newfoundland and Labrador, the territory took no position on the property question.
The rest of the provinces and territories have until Friday to submit factums to the Supreme Court.
So far only Nunavut, Newfoundland and Labrador, Manitoba and the federal government have filed their submissions.
Liberal Sen. Serge Joyal also filed a factum Thursday; however, the Supreme Court had not yet finished processing the document and could not release it.
Manitoba Attorney General Andrew Swan says the upper chamber is basically flawed and should be abolished, but he cautions that the federal government can't go it alone.
The province's submission argues that Parliament does not have the constitutional authority to enact significant unilateral changes to the structure of the Senate or to the selection of its members.
Swan says such changes require consultation and agreement with the provinces.
If the Senate is not abolished, Swan said, its members should be elected.
In 2009, Manitoba's all-party committee on Senate reform recommended the federal government administer and pay for elections of senators in the provinces and that these votes be held alongside federal elections.
A private member's resolution calling for the abolition of the Senate has been tabled in the provincial legislature.
Ontario, Nova Scotia and Alberta say they plan to file their factums Friday. British Columbia says it has been granted an extension until Sept. 6 to file.
In its submission, the federal government argues "it is constitutionally permissible for Parliament to impose term limits, provide for public consultative processes on Senate appointments, and remove the archaic requirement that a Senator" own at least $4,000 worth of land in the province they represent.
The federal Conservatives say they plan to move ahead with Senate reform — or even outright abolition — once the Supreme Court provides guidance over how they may do so.
The New Democrats, meanwhile, are calling for Senate abolition.
As the Supreme Court ponders the government's questions, a scandal over Senate expenses has cast the upper chamber in an unflattering light.
The RCMP is looking into the questionable expenses of former Conservative senators Mike Duffy, Pamela Wallin and Patrick Brazeau, as well as former Liberal Mac Harb, who has since quit the Senate.