B737-400
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Time Pressure; Workload
Aircraft Equipment Problem Critical; Ground Event / Encounter Loss Of Aircraft Control; Ground Excursion Runway
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification; General Flight Cancelled / Delayed; General Maintenance Action
Human Factors; Aircraft
We received paperwork; closed doors and went over our checklist; proceeded to taxi to Runway XX via taxiway Charlie. We were instructed by Ground to contact Tower. Tower cleared us for takeoff via Runway 22. We completed before takeoff checklist and the First Officer stated he would 'take it on the roll'.  I proceeded to Runway 22 and lined the plane with the center line and I then informed the 1st officer it is his aircraft. The First officer proceeded to stand the throttle up about 40%. We proceeded down the center line when he pressed toga and the plane veered hard left. The First officer stated he was pushing the right rudder but had no control. He took the throttle back and I applied brakes. I have the airplane and the aircraft slid off the runway onto the grass. We came to a full stop.  We contacted Tower advising them of the situation and were advised by Tower; emergency vehicles were on the way. Tower requested to know how many souls were on board and how much fuel was in the aircraft. We advised Tower 3 souls were on board with 17;000 lbs of fuel.  Upon seeing the first fire truck; we advised Tower we were shutting off the engine and leaving the APU running. I then spoke to Tower who connected me to the rescue vehicle; at which point I advised the First officer we were shutting off all power to the plane. The rescue vehicle arrived with stairs and we deplaned.
It was my leg the Captain lined up the airplane I told him we're going to taking it on the roll I advanced the thrust levers to 40% N1 and pressed the TOGA BUTTON The plane start rolling and then veer to the left. I was stepping on the right rudder to try to center the plane back but The plane kept veering to the left; and as a result we ran off the runway into the grass. My best guess would be the steering actuator or maybe engines not spooling up correctly. My reaction was I couldn't believe this was happening and that I had no control over steering the aircraft.
B737 flight crew reported loss of directional control during takeoff roll.