Alright so I did some digging using a friend, CE and the latest table(not linking it because it's Bad Stuff™).
The table I used didn't list item discovery directly so I had to search a bit for it. As expected, it is affected by luck and item discovery gear. Having another player didn't change it, and having the other player equip item discovery gear didn't change it either. Now I'm not a pro at CE but I tried to find places that used the item discovery value and what I think was the drop rate formula didn't have any changes when another player equipped I.D. gear.
First, I did 5 "cycles" of killing the 3 Silver knights in Anor Londo with no item discovery gear and noted the drops. Then I did the same with my friend, no item discovery gear. It didn't make any difference.
I did 5 cycles with gold covetous ring+3, Symbol of avarice and a crystal sage rapier and noted the drops. Then I did the same with my friend (who had no I.D. gear). No difference. He then equipped the same stuff as me. 5 more cycles, no difference. We did this again a couple of times with him as a white, gold, purple and red phantom and it didn't change anything.
As a last attempt, I used the Dried Fingers and summonned the max amount of players I could and got invaded. I killed the 3 knights. No noticeable difference in drops, no changes in CE.
Extra players of any kind (white, gold, purple, red), summoned or invading, do not appear to change item discovery or drop rate.