TL;DR When partied for empowered monoliths, only the “chooser” of the boss quest loses stability and gains Gaze of Orobyss on boss kill, but everyone gets to select a blessing resulting in possibly unintended extra blessing selections since the rest of the party retains timeline stability.
Here is the experience of attempting empowered monolith progress as a party of two:
My husband had completed some echoes in Empowered Fall of the Outcasts up to 130 stability. I had zero stability. We partied up, and I took a portal to him. From there, he chose echo nodes on his Empowered Monolith, and I was the “tag along” getting the choice of reward each time. We did not “take turns” choosing echoes.
Fast forward until we both had over 800 stability. He chose Altar of the Flesh and we completed it together. After completion, his game reported that he had gained 1 Gaze of Orobyss. My game reported that I had no stability and also 0 Gaze of Orobyss. It should also be noted that I was able to choose an empowered blessing.
At this point we disbanded party. I teleported to the End of Time and back to Fall of the Outcasts. When I clicked on the monolith crystal this time the game reported that I have 0 Gaze of Orobyss BUT I also have 861 stability. This seems to be bugged because the game previously reported that I had 0 stability.
I was able to take on Altar of the Flesh solo at this point, and when I completed it I was again able to choose an empowered blessing. This seems bugged but more in favor of the player and possibly an exploit. Upon completion solo, I did get 1 Gaze of Orobyss.
If this behavior is consistent, it means that in a party of four people, all four could take on the empowered monolith boss and choose an empowered blessing. Then 3/4 could do it. Then 2/4. Then 1/4. By rotating who is the “chooser” it would speed up group empowered blessing farming and seems exploity to me.
It seems like this isn’t the intended functionality and instead party completion of the empowered monolith “boss quest” SHOULD consume everyone’s stability but SHOULD also grant everyone Gaze of Orobyss.
I did not record or take screenshots along the way unfortunately, but I’ll provide any additional context or tech info if needed. I am completely certain though that I selected the 66% Grand Scales of Greed blessing first (replacing my 40% Scales of Greed) then when I completed it solo I selected 93% Grand Sight of the Outcasts since I need large idols for my build.
Thank you for making such a great game! Except for this one instance, my husband and I have had a very smooth experience playing as a party not feeling like either one of us was “losing out” on progress or anything like we do in certain other ARPGs. 
DxDiag.txt (163.8 KB)
Player.log (1.1 MB)