The Globemaster III is known in the Canadian air force as CC-177. Four of the aircraft are in military service after purchases made in 2007 and 2008.
Despite Canada's involvement in more recent years in Afghanistan, where the aircraft is used as a strategic airlifter, Ottawa has resisted calls for more purchases.
The Air Force Association of Canada in a policy paper called for more acquisitions, the Ottawa Citizen reported.
The policy paper, published by the newspaper, was developed by the association's air power advocacy committee as part of a lobbying effort.
Boeing is promoting the giant tactical transport in sales campaigns worldwide and is also pushing for what it calls a global sustainment partnership, in which the manufacturer looks after all aspects of the upkeep of the aircraft.
Canada's small fleet of Globemaster IIIs help provide everything from the rapid delivery of troops and cargo transport to oversized combat equipment from coast to coast and to anywhere else worldwide, the Canadian air force said on its website.
Rapid, reliable and flexible, the strategic and tactical C-17 is equipped with advanced digital avionics, has a maximum range of approximately 5,500 nautical miles and can carry a payload of up to 160,000 pounds due to its four Pratt and Whitney 2040 engines that produce 40,440 pounds of thrust, the air force says.
To illustrate the power of these aircraft, one C-17 can haul three CH-146 Griffon helicopters with refueling tanks, or one Leopard 2 tank, or as many as 102 paratroopers, Canadian air force says.
But perhaps most useful of all, the C-17's ability to fly long distances and land in remote airfields makes it a premier transporter for military, humanitarian and peacekeeping missions, the air force says.
Still there are no immediate plans to buy more of the aircraft but the advocacy group wants to change that.
"No one can predict when or where the next humanitarian disaster or global crisis will occur," the Air Force Association of Canada said, the Ottawa Citizen reported.
It said the recent earthquakes off the British Columbia coast, hostilities on Turkey's border with Syria and the unstable situation elsewhere in the Middle East present to Canada "clear reminders of the uncertain world in which we live."
It said Canada's need for air mobility in the arctic region amid competition from Russia and other northern powers also backed its view that buying more C-17s would be in Canada's interest.
"The Air Force Association of Canada strongly recommends the Canadian government acquire at least one additional CC-177 Globemaster III aircraft for the (Canadian air force) as soon as possible," the newspaper said, citing the group's policy document.
The U.S. Air Force says the C-17 Globemaster III is the most flexible cargo aircraft to enter the airlift force, "capable of rapid strategic delivery of troops and all types of cargo to main operating bases or directly to forward bases in the deployment area."
A single C-17 costs $202.3 million in fiscal 1998 constant U.S. dollars, the U.S. Air Force website states.
The price paid by Canada for its four C-17s wasn't revealed in Canadian reports and the price Canada may have to pay for a new model is also not discussed in recent data.