It really doesn't matter if you add an EBJD or any other cichlid, any new cichlid will be considered competition for space and dealt with as an interloper by the 1st JD.
Once the 1st addition takes over the tank as its territory (and 3 months is long enough to take over the entire tank), any cichlid you add after that is at a disadvantage.
Maybe if the other was twice the 1st ones size, the tables would be turned.
But adding cichlids piece meal to a tank almost always has dire consequences for new addition.
If you want a cichlid community it is always best to add them all at the same time.
If you added 10 new cichlids instead of 1, the aggression would be so spread out as to be inconsequential.
This also should be considered with any fish that looks similar to a cichlid (datnoids, leaf fish, etc).
None cichlid appearing fish, like tetras or live bearers are a different story, and not usually considered competition