Get 2 Sims, who live separately without other Sims, 2 pets each by either buying them in the pet store or relocating other Sims pets.
Have the Sims become friends and have the one who lives at the house that you don't want to become your pet house ask the other to move in with him/her. When 1 Sim moves in with the other, the moving Sims' 2 pets are left behind, leaving a vacant house with 2 pets. This vacant house will become your pet house.
Click on the vacant pet house and choose "relocate household" ($8,000). Then, select your 2 Sims that live together. When they move, they will bring their 2 pets with them to the pet house which already has the 2 abandoned pets, making 4 pets.
Relocate one Sim back to the newly vacant house ($5,000).
Get the Sim that moved out 2 new pets.
Have your Sim with the 2 new pets ask the Sim at the pet house to move in with him/her. This will leave the pet house vacant again, but with 4 pets.
Relocate your household into the vacant pet house, now you have 6 pets.
Repeat, repeat, repeat.
I hope this helps anyone who is looking to add a pet farm. My picture above is my current pet/hobby house. There are more pets than what you see in the picture. The dogs tend to hang out behind the house and the cats like to migrate towards the sidewalk. I'm taking a break from adding new pets, because I am using a lot of my LPs on my Mysterious Island. Once I make the volcano erupt, my next endeavor will be to add 30 black cats to my haunted house since I spend a lot of time in that house ghost hunting. Eventually, I will create a pet farm on an empty lot.
Please comment with any feedback or additional tips you may have for adding a pet farm.