We have been concierge guests on multiple cruises with the large dining room table and I cannot, for the life of me, think of any extra options offered from regular room service. There might have been options available, but we were never told about those on any of our cruises. Perhaps, the OP is referring to the possibility of ordering from the MDR choices if you have a suite with a table or Palo's if you are in a Royal or two bedroom on the classics.
We did, for example, have our freezer filled with Mickey bars (our request) on our last cruise. However, again, I would think if there were extra options, we would have been told.
I will also mention that concierge guests do seem to be held to the same standards as everyone else. For example, although we could get room service on the last morning (cold breakfast) on the classic ships, that option was not possible on the new ships. In addition, we were held to ordering from the MDRs and Palo during regular hours. No, you could not order a chocolate souffle from Palo at 9 am! Also, the last evening on our last cruise, we hit the same bottleneck of people calling for room service. After 30 minutes on hold to place an order, I gave up. I guess we could have had our concierge take care of it, but I hate to bother.
DWF