Yes you can. What type of CA closets you have will determine what prep work you need. For just an idea, subject to change once your actual surface is determined:
Step 1 - rough up the finish on the existing surfaces. Wash all dust off the surfaces and allow to dry.
Step 2 - prime. I have used Xim primer sealer bonder and also Zinsser Bullseye 1-2-3.
Step 3 - 2 coats of high quality paint. I use a small foam roller and satin or semi-gloss paint. You can lightly sand after the first coat to knock off any dust or particles.
Good luck!
Q