Plotties are what's known as a Closed Species. This means you can only make your own if you have a MYO (Make Your Own) Slot.
There are different slots you can choose from. They differ in what they include and how much they cost, but any of them will allow you to create your own Plottie. Some of them are: Standard MYO Slot, Epic Bundle, MYO Token, Fertility Elixir, Lab Kits, among others.
The Standard MYO Slot includes unlimited Common and Uncommon traits and 1 (optional) Rare trait.
You can buy MYO Slots in the Happy Bloom Shop.