Painting - Painting over deep red accent color

We painted our daughter's room a deep "blood" red. We were told when we bought the paint it was an "accent color" and would take several coats. That was an understatement. It took a coat of primer and 4 coats of paint. She has moved out and we would like to paint over it. Can we start with a coat of white primer? It was a satin finish paint.

Thanks

Denise

The actual color was "Scarlet Fire" from the American Traditions line at Lowe's.

It is almost always a good idea to use a primer to help kill the color of a dark paint. It won't hurt to use two coats. Zinsser 123 will do a great job. There are others out there, it is just my favorite.