Is it possible to hold two AOC's in the Army? Such as 72D and 70H? Such as a primary AOC and secondary?

It may be possible in the Army Reserve or National Guard but not on Active Duty. A 72D is a scientific AOC wit specific degree and credentialing requirements. Where as as 70H starts as a 70B. Once you make O-3 with 6-8 years of service you got through an AOC Designation board (Active Only). In the USAR you could most likely hold the 72D AOC with the 70H as a secondary AOC. Usually only 67J (MEDEVAC) pilots do this on Active Duty. It’s common in the Reserve to hold more than one AOC as a 70 series. Example, 70H, 70K, or 70F. No 70A in the USAR.

Not sure if things have changed since I retired (2011), but back then the only AOC allowed to have a second was 70J.

I’m in the Guard and I hold both of the listed AOCs; 70H is my primary, 72D is secondary. As mentioned previously, the active component doesn’t allow this configuration.