No amount of additional coats of any kind will increase adhesion of the first coat to the plastic. That first coat needs to really grab the surface of the plastic.
I almost always use a primer. My current go-tos are either Tamiya white or gray in a spray can, or Badgers Stynylrez through the air brush.
Clean the part thoroughly after handling and before painting. Natural oils in our skin are disastrous to good adhesion.
Bill