Let me first confess that I am not a cat person and then let me apologize for the long history. My son adopted a juvenile cat with a lot of confidence. I had an adult basenji (8 yrs old). We did not live together, but I would bring my basenji for brief visits over the course of a couple of years, so the cat and dog knew each other. Fast forward several years. My son joined the Navy and nobody else in the family would keep the cat, so cat came to live with us. The basenji I had was quite elderly by that time. Dog and the cat got along just fine - not cuddly, but no blood shed. The basenji passed away just before his 15th birthday. The cat and I lived alone together for several years until I retired. I adopted a 3.5 yr old basenji who wanted to chase and bite the cat. It took me over 8 months, but I succeeded in getting them to coexist (and could even trust them alone together). The absolute key is TIME.
First, I kept the cat (with litter box and cat tree, etc.) in the guest bedroom with the door closed AND a walk thru gate about 3 feet away from the guest bedroom door. The purpose was to get both critters accustomed to the smell and sounds of each other.
Once the basenji finally stopped trying to find a way to get thru the gate to the door, I propped the door to the guest room open a few inches so the cat and dog smells and sounds were stronger.
After the basenji ignored the gate/propped door, I opened the guest room door enough so the cat could get into the hallway. Cat would come to the gate and the basenji would go crazy, but eventually, he figured out he wasn't going to be able to get to the cat, so he got used to seeing and smelling the cat up close.
After a couple of months, the cat would venture out (thru the built in cat door that I modified so only the cat could fit thru and run to safety, but keep the basenji out). This resulted in many wild chases thru the house (some items got broken) but the cat would either jump up high or get back behind the gate where he was safe.
In addition to all the steps above, every day, two or three times a day, I would put the basenji on a chain leash, attached to something very heavy or to a door, and bring the cat to the couch and I would give them both treats and praised the basenji when he behaved calmly and unaggressively towards the cat. The basenji would get a reprimand or strong "no" when he tried to lunge at the cat.
The cat would venture out to the living room in the evening while the basenji and I were on the couch. I held the basenji's collar and made him stay with me while the cat roamed or joined us on the couch.
Finally, the cat could walk across the room without being attacked, but if the cat ever ran - the chase was on! The cat would stop, hiss, puff up and swipe at the basenji, but that never phased the dog once he was in "hunt mode".
I kept kitty litter box and cat food in the guest room where the basenji had no access.
Your situation is complicated by multiple cats, however, it might be easier for you because your basenji is younger. Regardless, you can expect it to take up to a year (and maybe never) depending on the prey drive of your pup.
A friend of mine had a dalmation that she kept chained to a piano for years (of course there was time out for walks and play time) because her dog wanted to eat the cat.
P.S. After about 3 years, the cat escaped thru the front door and we never saw him again. My guess (and hope) is that he found himself a home without a dog.