Please define "rare loot pools". Usually color indicates rarity. So it sounds like you're saying that in theory, a 4 player coop game would drop the most legendaries.
Basically, when you fight a boss they have multiple rolls that determine what they drop.
Ex. One if for a pool of loot. The second is for what will be in the pool.
Let's take Doc Mercy who drops the Infinity.
When you fight him, he generally drops a green item. That would be his "regular pool".
Sometimes, he drops better than green. That's his rare pool.
After pool is determined, actual loot is then determined.
This is just a simplified example. There may actually be more than 2 pools, and rare may not necessarily suggest blue or better items. Just pools that they don't "commonly" drop.
In the simplest terms, more people playing = better chance of getting the bosses to drop their best loot. Whether it affects stats of said loot, I have no clue. Probably not. --- "It's like people using the internet have never heard of the internet." - SadHillShowdown Gamefaqs member