What's the theoretical maximum density of a galaxy? In watching this Hubble video on Omega Centari it got me thinking about how dense a galaxy can get. Do we know how dense a galaxy can get?

Are there any good resources on reading more about very dense galaxies?
As a general rule, galaxies aren't very dense at all, though precise numbers are impossible, rough estimates can be made.

Mass of the Milky-way:  with it's dark matter halo, about 6 x 10^42 kg

Volume of the Milky-way (per Wikipedia) about 3.3 × 10^61 cubic meters, or, 3.3 x 10^52 cubic km.   

That gives us a rough density of the milky way of about 1 kg for every 5 billion cubic km.   That's obviously not very dense.   There are probably denser galaxies out there and larger galaxies, but the overall density is going to be very low, even for the densest galaxies.   Space is, generally speaking, mostly empty.

Even in regions that are so called "densely packed with stars", if you measure the density in the traditional way, mass to volume, you end up with very low density, 1 kg per thousands if not millions of cubic km.   On earth, that density of air would essentially be a vacuum.