So after season 2 ended, I went back and watched the first two episodes of Season 1, and I saw Irving in a whole new light.

I'm now considering the possibility that Irving reintegrated long before Petey, and may have even encouraged Petey to follow in his footsteps.

Consider this:

-In season one, Petey refers to a group who is trying to take Lumon down.
-In season two we see Irving keeps calling someone. One of those phone calls includes the phrase "I guess you're not picking up."
-Petey's cell phone rings lots of different times before Mark answers it (could Irving be calling Petey's cell phone, not knowing that Petey is dead?)
-Irving has a very odd expression on his face when Helly R. joins the MDR team in S1E1. Like he knows exactly who she is.
-Irving urges Mark to keep the group photos on the desk as long as possible. It MAY be because he knows that the map to the Severed floor is on the back of Petey's photo, and he wants to give Mark every opportunity to find it.

I don't know. Just thinking.

I'm now kinda hoping Season 3 includes a flashback episode all about Irving.