The amendments, to be tabled by arch Holyrood critic and Scottish Labour MP Brian Donohoe, include a call to abandon list MSPs entirely so that the parliament is represented solely by constitiuency-based members.
A second amendment to the Act proposes to outlaw list MSPs from opening offices, as many have chosen to do. Those offices have been described by former Presiding Officer Sir David Steel as a "thinly disguised subsidy from the taxpayer for the local party machines".
The changes can now be voted on at Westminster as a result of the new Scotland Bill, which would give Holyrood substantial new tax powers. The Bill has opened up the original Scotland Act, allowing MPs to attempt for the first time to change it.
Donohoe claimed last night that he had substantial support but his move prompted outrage from SNP MSPs, who would be among those hardest hit by the reform.
The Central Ayrshire MP said last night that shutting offices "would put a brake on list MSPs interfering in the affairs of individual constituencies and building power bases around the country".
Donohoe said he would also be looking for support at Westminster to create a new voting system at Holyrood, where two MSPs per constituency are elected and list MSPs scrapped.
The relationship between list MSPs and MPs has long been fraught, with MPs claiming that the MSPs are "invading" their patch.
Kenneth Gibson, the SNP MSP for Cunninghame North said last night: "Labour must distance themselves from Mr Donohoe's disrespectful suggestion immediately."