Plecos roughing each other up is common. I've kept many plecos of varying species and they all do it. The tank set up does vary how often they get into a domination match, but they still do it every so often, even if you have a ton of caves, low stocking and large tank. Although in pleco tanks, containing bunches of plecos, they don't fight much.
The fighting doesn't stress out the fish too much nor do they fight to the death, but they can bump each other around and end up uprooting plants/substrate, knocking over decor/hardscape and causing other fish to flee the area to get out of their way. Their colors can fade and often end up with split fins, but nothing much more than that before one of tem retreats. They don't stress too much over it, no real rapid breathing or anything like that, but they can end up staying in their shelter more often to avoid another scuffle, but I can imagine if they had a choice, living alone able to move freely around the tank without the need to get into a tussle would be preferred and less stressful.
I really don't like my fish fighting so I'm always picky about that stuff. The plecos would mainly just fight amongst plecos. They do defend themselves against bullies (larger fish). They are peaceful with other fish, even the bottom dwellers, although some have plecos that are food hogs, so they do fend off other fish from the food until they get their fill (some people, most don't have this issue and the pleco happily and gently feeds along side other fish, even nano fish).
If the attached thumbnail above is your tank, plecos want caves, places that provide shade so they can get out of the light. From the looks of it, there isn't really any cave. You may end up with a pleco digging under some driftwood to form a cave.
Oh, just reread one of your post above. In my experience, juvenile plecs are usually left alone or don't pursue fighting at least. Well at least until they get more mature, then it will start challenging the other plec. Adding the juvi into the tank with the larger BN should be just fine, like I said, they don't kill each other.
You can try it out if you want. If you did wan't to keep more than one, I would suggest just sticking with a mated pair (M/F of same species). Look into Green Dragon BN if you want, sort of a mid point between the two haha (BN and green, although not as nice of a green as the phantom)