The Horn of Abaddon, having once been the central base of an infernal death cult, has clearly been designed with security in mind. You cannot find any way up from the first level to the second that does not involve exiting the entire temple and taking an entirely different root up the side of the mountain.
The second floor is clearly designed for superior defense relative to the first one. The approach staircase is winding and narrow, and the narrow entry hall stretches for forty foot between a pair of guard rooms that cover it every inch of the way with overlapping fire arcs. There is also a pit trap midway along the hall, now jammed open by the passage of time and bridged by a crude set of logs (it appears to drop intruders somewhere on the first floor), and there is a half-wall at the end to provide a superior position for defending troops. When you enter the floor proper, you see why.
This whole floor is evidently designed to meet the needs of the true priests of the death cult. Blasphemous murals cover the walls, showing numerous scenes from the cult's history and the various profane rituals they have performed. Interestingly, some of the murals are so detailed and intricate you wager you could likely duplicate some of those summoning rituals yourselves, though it would take some time.
The centre point of this level is a proper temple-shrine chamber in the east wing. Six stately pillars rise into the air, surrounded by carvings of carrion birds and plague daemons, forming a processional that leads right up to the foot of another throne much like the one on the floor below. This one is inscribed with the abyssal symbol 'Rah'. Interestingly, it appears that the pillars match up with similar (though less ornate) constructions on the floor below. Structural supports, perhaps.
The west wing of the floor appears mostly given over to acolyte quarters. They are mostly empty, save for one which holds a single statue of truly exquisite craftsmanship. It depicts what must have been a member of the cult, standing in the centre of the room with a spiked flail brandished menacingly.
From one of the other chambers, you think you can hear the sounds of movement.
A quick search of the floor yields no way up to the third level. There must be one, since it seems doubtful the priests would have willingly gone rock climbing across the face of the Horn every time they wanted to go up there, but it has evidently been hidden. The closest you have to a passage up is a holding cell which seems to connect to a pit trap on the floor above, currently sealed.