Preheat your oven to 350°F (175°C).
Grease and line three 8-inch round cake pans with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, and salt.
In another bowl, mix the dairy-free yogurt, buttermilk, melted coconut oil, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Reserve one-third of the batter in a separate bowl and mix in the cocoa powder and additional ¼ cup plant-based milk to create the chocolate batter.
Alternate spoonfuls of vanilla and chocolate batter into the prepared pans. Use a knife or skewer to gently swirl the batters together to create a marble effect.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.