More colorant....probably no.

I'm having a brain-gap here, but the "recommended" tinting-limit for BIN is 1 or 2 oz's (I THINK it's only 1 oz.).
* That would typically land you in the Beige/Khaki range.
* I would've done a "gray" primer for ya. It's typically a darker color than is acheiveable using an actual "color" formula.
* You could maybe "over-tint" it slightly. If you could post the formula (if it's on the primer can...), I could tell ya how much more colorant could be added. It could be OK just to add some more Black.
* Deep Brown/Black colors are relatively more opaque vs. the Reds/Magentas, due to the nature of the colorants.
* You'll still need 2 FULL COATS of the actual paint obviously...even if the primer was magically only slightly lighter than the color!!!

Faron