You are correct. There is no OVR parameter for the API code. However you can apply a load factor to the appropriate combinations to get the same effect. For example instead of multiplying the allowable stress by 1.33 you can factor the loads in the combination by a factor of 1/1.33 = 0.75 as shown below
LOAD COMBINATION 100
1 0.75 2 0.75 6 0.75
where 1, 2 and 6 are primary load cases and 0.75 is the applied load factor.