We have 3 Basenji's now – a nearly 12 year male, Ramsey which we've had since a pup, Bonnie, a 11 month old female, also since a pup, and now Smitty, a 10 month old male which we got a month ago. We had to put down our 14 year old female earlier this year.
At first all seemed fine once we got Smitty, then on the 3rd day of having him, he and Ramsey got into outside at the fence (another dog came by). I stood about 30' away and let them work it out. Smitty backed off, but not before getting bit on the nose and Ramsey on the ear. However, since then Smitty has gotten more and more assertive and isn't backing down.
Usually fights break out when Smitty and Bonnie, are playing. Ramsey nervously follows them around grawling as though to say "knock it off you 2". Once Smitty invades Ramsey's space a fight always breaks out. Ramsey starts it. Now neither backs down until I pull them apart.
When the younger ones are tired they are all fine together. The males can sleep in the same sun spot during the and even chew on treats in the same room. I try to monitor their play when I can and often crate Ramsey when they are running laps around the house. Still I have to be ready any second to bolt across the house when they're loose -- like I did just a few seconds ago!
We have 2 little kids so I don't want them to get in the middle of anything and also I don't want either dog badly hurt (they could have gotten a couple stitches from their first fight -- poor guy will have a nice scar now). We have even talked about giving Ramsey up to a family we know, but would hate to loose our buddy of 12 years -- already went through that once this year!