Mechrite Red should do well to cover most color primers.
That being said, it can't hurt to thin it some in order to get smoother coverage and prevent obscuring details.
When I go to paint red on a model (a Blood Angel for example) I try and use a light grey primer. This helps me see the detail on the model and keeps me from having to paint more than one good coat with some touch ups.
Here's how I paint Blood Angels showing how I use Mechrite Red on my models.
http://fromthewarp.blogspot.com/2010/04/blood-angels-how-to-paint-red.html
If you're up for stripping your model, a light grey primer might help out.
If not, you could always try a heavy drybrush of light grey over the black primer to help lighten it some.