How does a DC-10 flight engineer manually raise the cabin altitude?
Tip: accident investigation reports cover the system controls related to an accident. The one in question is here (ntsb.gov), from which:


  According to the March 20, 1994, edition of FedEx’s DC-10 Flight Manual, page 8-2-2/8-2-3:
  
  
    Cabin pressure is controlled and maintained by metered release of conditioned air in either an AUTO, SEMI-AUTO, or MANUAL mode…. The cabin pressure controller maintains the desired cabin pressure in relation to the altitude set…. In the AUTO mode, cabin pressurization is automatically controlled during takeoff, climb, cruise, and descent conditions to the lowest cabin altitude compatible with aircraft and flight requirement.
    
    When MANUAL control is selected, the control wheel engages a locking mechanism to secure the outflow valve in its existing position. After selection, manual control is achieved by pressing the control wheel inward (to disengage the control wheel locking device) and rotating the wheel to position the outflow valve to attain the desired cabin altitude. When the control wheel is released, the outflow valve is again locked in its existing position. Selecting the valve at more than two-thirds open can cause a negative pressure and create a noise in the cabin. At touchdown, the Second Officer [flight engineer] must manually depressurize the aircraft. [emphasis added]
  


Regarding the outflow valves, see:


What is this device below the door of a 737 (and other aircraft)?
What are these &quot;portholes &amp; panels&quot; on the fuselage of the Omega Tanker DC-10?


And the aforementioned wheel and readout:


Source: wikimedia.org