Issue of Anatomical Interpretation - a case for 1 rider
As Valley Lad notes, the carrying capacity of a giant eagle is sufficient to convey a good number of players - the main limitation is "appropriate anatomy".
A riding horse has the same size and strength as a giant eagle. Horses have been bred for thousands of years to have an anatomy ideal for riding, and yet two riders on one back is quite a squeeze. A giant eagle has no such pedigree, and we might be able to assume that much of its "large" size is owed to its wing span, where as a horse's size is almost all torso. Note that a medium sized creature occupies 5'x5' area on a battlemap, and a large occupies a 10'x10' area.
The only other guidance on mount qualification is that it must be one size larger than the rider. A medium creature (human) can ride a large creature (giant eagle), for example. There is no RAW rule against this, but it intuitively feels wrong for a mount to be ridden by many creatures only a single size category larger than it. Four Medium-sized creatures on a Huge mount perhaps, but on a Large?
However, if all of the players were put in a basket carried by the eagle, I believe there is no question of anatomical limitation: in that case the number of passengers would only be limited by carrying capacity.