Currently we are developing enclosures in an isolated "system of systems". Our overall system is fed AC power and converted to 28V with an off-the-shelf converter. Currently the enclosures we are designing each have a PCB internally and currently these PCB's power supplies are tied to the same ground (dashed red lines shown in the below diagram). My project manager is worried that this connection will cause problems when we go to test these items for EMI and he wants to remove these connections and have isolated lower voltages. I'm contending that the grounds should be connected because there won't be any common reference for the single ended connections between each enclosure. Also, some of these circuits use the 28V input as a reference as some of the signals are 28V. Do these lower voltages need to be isolated from the 28V?
Since you are showing analog and signal grounds being connected between the two boxes, connecting the power grounds together is not a great idea. You are inviting ground loops.
That said, if your boxes are at all separated physically, and your interconnecting signals are low voltage/ high impedance (10 volts, a few k), you will be very well advised to use differential transmission for your interbox signals. Particularly when dealing with 28 volts systems, the IR drop on the power lines can produce significant voltage offsets. Since your 28 volt return is labeled ground, if your boxes are likewise grounded you need to be extremely careful of your internal ground routing. Make sure that your signal and digital grounds are isolated from case ground by several k.
Set your system up so that you can easily swap between several different connection schemes. (like with disconnectable grounding straps, resistors you can easily clip or solder on, etc) Try them all out at home and see how well each one works.
When you go to test EMC, have your wits about you and test the most preferred configuration first. If you fail, go to #2. If you fail, go to #3. If you keep failing, start throwing ferrites in the system.
This is the way it's done in 'real life'. A lot of engineers get a sense for things, but without being able to actually LOOK at your setup and consider all the random factors you've probably left out, any specific advice is kinda worthless. Besides, even engineers who know what they're doing screw it up and have to reconfigure slightly at the lab.
The previously mentioned advice about ground loops is legit, so you should take that into consideration if you're having noisy signal issues.
I second Daniel's scheme, which is to prepare for contigencies.
Ideally, all blocks of each enclosure will form a Star ground to the chassis. Then, each enclosure will form a Star ground to the external supply. The supply should then be earth grounded.
You should carry ground between the enclosures along with the IO lines so all references are common. This also reduces the loop area for the ground return, thus reducing emissions.