The NDP has argued that taxpayer-paid employees assigned to the satellite offices work only on behalf of New Democrat MPs in Quebec City and Montreal.
And the party has contended that taxpayers actually save money through the arrangement because staff don't have to be shuttled from Ottawa to Quebec to organize or attend local events.
The New Democrats say they expect the majority of MPs from the Conservative and Liberal parties sitting on the board of internal economy will rule against them in the meeting, which is being held behind closed doors.
Hoping to prevent that from happening, the NDP plans to table a motion at the meeting to make it public.
It also wants the board abolished.
"The NDP believes that the only way to have real accountability for the BOIE is to replace it by an independent body," said NDP House Leader Peter Julian.
"But until then, the only way to make it more transparent is to lift the veil of secrecy and to ensure that all meetings are open to the public."
The secretive board recently ruled that the NDP broke rules governing free mailing privileges and ordered the party and MPs to repay $1.17 million.
The New Democrats are fighting that ruling in court.