You could use black gesso or other dark pigments mixed into the ground. Then the transparency of your violet/purple paints will not be trying to overcome a white background, requiring less pigment.
If that is not an option then mixing (more opaque) primary colors to get the purple you want is an option. Just make sure the tone (lightness) of the red and blue pigments are close (lighten the darker of the two with white) and that you match cool with cool and warm with warm to avoid muddiness. This gives you the advantage of more control and variety in the final color as well.
Are you mixing the Dioxazine purple with titanium white to get your tone or using straight up and relying on its transparency to the white ground to get the tint you want? It should be strong enough to make a good tinted body color and that should give you the cover you are looking for.
ie. you may just be using your paints too thin to get any body color from them.