LEMME STEP RIGHT IN-
 
A police dog is not helpful to forensics. Forensics at its core is lab work. Lab work, such as analyzing fibers and so forth, in a sterile lab. Dogs would interrupt this, and do not provide any benefit to the lab-worker. Dogs would ruin the environment, spread fur, and can and probably would run around destroying valuable evidence. This is why dogs are not in the labs. K-9 Units use dogs, Forensic Units do not. These are different units with different purposes.
 
If your character was a member of K-9 Unit, and oh, had their dog to cover up sniffing of drugs at the airports and such, that would be sound. But it is silly for Forensics to have one.
 
And onto the duo.
 
The buddy cop dynamic is a simple and time-honored one. It works by virtue of two cops, who act as foils for each other. Sometimes they are more similar than different, sometimes they are far more opposites. It is a duo. Not a trio. Quartet? I don't think so.  
Imagine Pinky and the Brain. This is another system that works via the 'two partners' system. Someone at Warner Bros thought it would be a good idea to add a third. The writers showed how doing so would flaw the dynamic, by adding Larry. Unfortunately Warner Bros Corporate didn't get the message and made Pinky, Elmyra and the Brain.
 
I don't want to fester on about Pinky, Elmyra and the Brain. Figure the third point was covered enough, our dudes are Vice. Vice does not engage with Forensics, and Forensics does not engage with Vice.