Some info that is not on the wiki.
So apparently, you can summon blue phantoms to help you in the fight as long as you stay within the first room past the arch (without going up the stairs whatsoever). Once you have blue phantoms with you, proceeding up the stairs will trigger the game to seek out a player to fight against you (or in the case that it fails, summon the standard NPC boss.) If you begin summoning a player and then begin to run up the stairs before that player materializes in your world, they will see a summoning failed on their end.
If you have 1 or more blue phantoms with you when the boss black phantom (NPC or human) is summoned, the boss will be significantly harder depending on the number of blue phantoms you have with you at the time. I assume that if the boss is another player, the game will seek in a higher level bracket. I assume this is the case because once you have an invading black phantom waiting, you cannot summon anymore blue phantoms, even if you go down to the bottom room and see an active soul sign (all summonings will come back as failed). I don't know by how many levels the black phantom player increases for each blue phantom you have, but I know there is definitely a level increase. I also do not know what happens if your blue phantoms leave after you have a black phantom player locked in (do you get to summon another one to replace the one you lost? or do you just have to take on a super hard player by yourself?)
The alternate theory is that the boss phantom has his or her stats scaled up according to how many blue phantoms are in the world at the time of his/her invasion. This seems unlikely though, because I have fought numerous battles as the Old Monk and have never encountered more than 1 player entering (at level 50-80). Most likely due to the fact that I was not high enough level to take on more than 1 opponent. Though I find it unlikely, it is still within possibility.
I find it actually kind of cool that you can fight higher level players by bringing in some backup. I would also like to see what it would be like being the 1 black phantom fighting against 3 other people.