is not possible in the American, congressional system
, unlike the Canadian parliamentary system
In Canada, the executive--the prime minister and cabinet--is dependant upon a majority vote of the legislature or house of commons. Thus, if no party has a majority in the house, then it must seek the assistance of another party.
In the congressional system, the executive does serve at the pleasure of the legislature--though that is something of a myth today--but serves for a fixed term, no matter what--short of impeachment and removal.
Two parties working together not need to be in a formal coalition, as frequently happens in the Parliament of Israel--the Knesset--where members of the junior party (or parties) take cabinet positions.
Simple cooperation, as given by the New Democratic Party to the Liberal Party of Canada, that enabled Lester B. Pearson to be Prime Minister was simply an agreement on an agenda. No New Democrats took positions in the cabinet. But generally progressive policies were enacted--such as medicare.
In Ontario, David Peterson of the Ontario Liberal Party, and Bob Rae, of the Ontario New Democratic Party, also simply cooperated to oust the Ontario Progressive Conservative Party under the recently deceased Frank Miller.
And when Bob Rae came to power there was little support from the Ontario Liberals.
Coalition government is not a common occurance in Canada. There was the Union Government of R.B. Bennett during World War I, but that is about it.