I've seen a few tutorials and WIPs where people are using a black primer beneath the metallic paint. So I decided to try it out, and wow! It makes a difference. It gives it more weight and substance somehow. It makes it really look like metal, not a plastic imitation. I really like it.
Preparing for more testing:

Black, grayish, and silver, in that order:

I waited for a longer between layers, and gently sanded the gray layer before applying the silver this time.

Black and two layers of silver:

Doing two layers of silver made a difference, but I think I sprayed the second one too close so it wasn't quite as smooth and even.

Comparison - Silver alone and silver with black underneath:

Comparison - Gray/silver with and without black:

The gray by itself really isn't my favorite:

Conclusion: Right now it's a tossup between the gray + silver and the two silver layers on top of black. I like the darker sheen of the gray/silver. But I'll have to be careful it doesn't come off as glittery. I think the sanding helped. The smooth color of just the silver on black is nice too.