more gain = more dynamics or less?

The answer is you want to MATCH cartridge output level to phonostage gain in order to attain the best SQ . If the phonostage doesn’t have sufficient gain for the cart’s output level, the signal will be noisy and the dynamic contrasts you’re seeking will diminish as you are cranking up your preamp volume to compensate and get an acceptable listening level. If the phonostage has too much gain for the cart then the phonostage becomes susceptible to distorting during peaks.

So without going into all the details, is it possible to generalize whether more phono gain creates more dynamic headroom, less dynamic headroom, or the same dynamic headroom?

Without going into all the details, you say? Okay.

You're talking about several different things that are sort of related, but not really. 

Gain is simply a multiplication factor. Its usually measured in dB and you can think of it as whatever comes in at XdB comes out at 45+XdB. Like that. 

Dynamic headroom, you inadvertently brought up headroom which is a completely different thing altogether. What you probably meant is dynamic range. Headroom is the ability to briefly go beyond a normal range. Dynamic range is the difference between the loudest and quietest parts.

In practice, and without going into too much detail, what you really care about is making sure the phono stage has enough gain to provide your preamp with a decent line level with your given cartridge. You also want to make sure your cartridge doesn't have so much output it will overload your phono stage. Anywhere in between those two extremes and you will generally be fine. 

Very helpful guys and thanks for keeping it high-level. I think my basic question is answered which is that inadequate gain can cause limited dynamic range. So I will seek the sweet spot in the middle.
Thanks!

My goal is to add enough gain at the phono stage to match the input sensitivity of my amplifiers preamp stage. My Parasound HINT preamp input sensitivity is 300mV, so setting my Nova II gain at 56dB gets me about 320mV, close enough.
This gets me very high resolution and extended dynamics from the Lyra Delos.

I think this is something that many MC users neglect to think of, so they add as much gain as possibly just so they don't have to turn the volume dial up past their "normal".