If you're having another circuit pass through the box, without splices ... I see no need to tie that circuits' ground wire to the box. You've already got that box bonded. Whether you have transformers, generators, multiple service drops, whatever ... the grounds of all the systems are supposed to be tied together at the sources. If they're not ... I'm not sure you want to do that at some remote, unknown box, using tiny wire and a little wire nut.
Even if there is no splices in the box does not mean the wire will not short out downline from the box. Although the ground from the seperate system may not be comprimised, by tying them all together will only improve the grounding system, not hurt it.
Now, let's assume that you have two separate systems in the box, both with splices. One word comes to mind: PARTITION. Isn't that box supposed to be partitioned? Even when the one system is 277, and the other 120, it's possible for there to be more than 300v. difference between the two (phase differences). With the box partitioned, I can see where you would make separate bonds to the box.
I do believe that the intent of the partition is to insulate the exposed screws that are in close proximity to one another in the box. depending on the phase configuaration between the 120 and the 277 circuits, there is potential for the voltage to be over 300 volts that could in theory if the conditions are right to allow arcing between the two. It has nothing to do with the grounding.
Why have more than one wire nut tying the ground wires together? Well, wire nuts are limited in their capacity, and it can be a challenge making a good connection of five or six wires. You've got to start thinking about box fill at this point.
I start thinking about wire fill when laying out the work. I use the 6 P's. Prior planning prevents piss poor performance. typically in new construction, the few wirenuts I have to use there are never more the four wires in them and my boxes only have the bare minimum wire count. Anything else is a waste especically with the cost of copper and plastic.
The white wires ought to be kept separate in the box, joining only at the panel. While the code might allow some wiggle room on this point, you're introducing an opportunity for all manner of bad things to happen.
The neutrals from seperates services are rarely tided together even at the service. A building that have multi-voltages are typically fed with one voltage at the service. The lower voltages comes from transformers on-site that typically derive their own neutral at the transformer. Granted if the neutral from both the primary and secondary are tied together, then the neutrals is not seperate. I do not ever recall seeing the neutrals tide together both on the primary and secondary on power transformers. I have on buck and boosts, control, and auto transformers but that this is out of scope of the OP.
As for the neutrals on the seperate systems having a little wiggle room in the code, can you clearify what you mean on that?
