It is VERY state specific. In some regions of the country, it is possible -- and even likely -- to get 3 MOC noms to a single SA and/or to get noms to multiple SAs from the same or different MOCs.
In other areas (typically, but not exclusively, those that are competitive in that there are more qualified applicants than nom slots), some or all of the MOCs may "get together" to limit the number of noms any single candidate can receive.
That can take the form of only giving one nom period to any candidate. Some go so far as to say that, if you have a Pres nom, they won't give you an MOC nom. Or it can be more "relaxed" in that a candidate will only get one nom to a particular SA but can receive noms to mulitple SAs from different MOCs. In some cases, the limits will only apply to a single SA if, for example, that SA is extremely popular in the state/district -- so only a single nom from all MOCs to that SA but maybe multiple noms to a "less popular" SA.
Sometimes only 2/3 MOCs get together and the third is a "wild card" -- IOW, will give noms to whomever he/she wants to even if the other two MOCs "ration" the noms between them.
The practices can and will change when there is turnover among MOCs. Also, if the MOCs are of the same party, they MAY be more likely to take the same approach; however, this is not universally true and this is one area where they may "work across the aisle."
The bottom line is that every situation is unique based on the proclivities of the MOCs where you live -- and even then, they can change their approach from year to year and the approach can change when the identity of the MOC changes.
The SAs have a pretty good idea of how each state works so, if you're in an area where one nom is the norm, the SAs know this and you won't be at a disadvantage when competing against those from areas where 3 noms is the norm.