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I understand the dimensions - the run is 6.7 x 2.5 feet (16-17 sq ft), but the coop/sleeping area looks to be about a third the length of the run and 2.5 ft. deep (for about 5 sf).  The height doesn't figure into square footage.
Generally, standard size chickens do best with at least 10 sf of run space per chicken & 4 sf of indoor coop space per chicken - banties need about 1/2 that space (5 sf of run space & 2 sf of indoor coop space per bantam chicken).  The coop you ordered looks VERY nice and perfect for about 3 bantams.  It's just on the small size for more than that.   Three bantams would need about 6 sf for the coop & 15 sf for the run - you have about 5 sf inside the coop & 17 sf for the run.  
It's a plus that the nestboxes are on the outside and don't take up any coop space.   You can always try putting a 4th one in there and if they seem overcrowded, rehome one of them later.  If you do enlarge the run  and they won't be staying inside other than to sleep or lay eggs, you should be fine with 4 of them.