I had some trouble with large groups for a family reunion in February (one group of 16, others of 11). I had no problem with an Ohana reservation of 11 and Cinderella's Royal Table for 11, but ran into trouble with Via Napoli for 11 and Liberty Tree Tavern for 16.
For Via Napoli and Liberty Tree Tavern the Disney dining rep made me multiple dining ressies for the same time (or close to the same time) and recommended I contact the restaurants closer to my trip to combine them. I have a phone number for Via Napoli to negotiate a table for 11 from my tables for 9 and 2, but will have to stop by LTT (no phone # available) to see if we can combine our tables of 11 and 5.
I wish I knew about asking for group dining--I maybe need to call back and try that.