I am not 100% sure. Here is what I think. Others please feel free to disagree.

I think there is a dual hierarchy. Think of a little pyramid on top of a bigger pyramid. Or a tiny building sitting atop a big building.

At the very top top is: Boss- Johnny DiFronzo, Underboss- Peter DiFronzo, Consiglieri- Marco D'Amico. I do not think Andriacchi is active anymore on any level. I don't really think Johnny or Marco are really active, other than running very (almost legitimate) lucrative enterprises such as Aruba and high level sports betting. However, like Accardo, I do think they have final say on major things in the post Marcello era.

I think when Marcello got out in the early 2000s, he effectively began running a shadow management operation. I think the taking out of Chiaramonte in 2001 caused DiFronzo & Co. to take a step back and some type of power sharing agreement was reached. The disappearance of Zizzo in 2005 and the attempt on Sal Cautadella probably had to do with the power struggle.

When Marcello went away, that effectively eliminated the "two tier" Outfit. I do think now DiFronzo and D'Amico have final control over major major decisions, but day to day operations are run by Sal Cautadella.

Here is what I think the structure is now below the DiFronzos and D'Amico.

Street Boss- Sal Cautadella
Street Underboss- James Inendino
These two are Cicero Group 1.

Capo- Salvatore DeLaurentis (Cicero Group 2)
Capo- Frank Caruso (Chinatown/26th Street)
Capo- Albert Vena (Grand Ave. somewhat active)
Capo- Peter DiFronzo (Elmwood Park- largely inactive)

The reason I do not think Solly D is a street boss or underboss is because he gave orders directly to Paul Carparelli. Carparelli may or may not be made, but those orders would not come from the top.