I say that common mode range is the range over which your
design meets spec. All of them. Unless you and your customer
agree otherwise.
It's much easier if you attach your VCC and VEE (VDD and VSS)
supplies to a third, VCM supply instead of ground. Then you
can sweep or step that and not have the signals moving away
from reference ground. You will see dedicated op amp ATE
product test programs work this way, so that they can make
best use of the range/resolution tradeoff inherent in pin cards.
For DC you'd expect the thing to meet Vio, AVOL, IIB/IIO.
For AC, you want to see the same GBW product and no
big change in phase. And be sure to run a transient sim of
some sort especially if it's got bipolars in the first stage to
see if there's a saturation hangup near one rail or the other,
or maybe the tail source is getting choked but maybe not
visible in small signal / DC.