Transformers are sized to permit 100% of their rating therefore 278 Amps (100080 watts) of 208V is avaliable for the 3 distruibution panels to share depending on connected load at each panel. In theroy it would be possible to load up the distribution panels (even following the 80% rule) to exceed the 278A output of the transformer but doing so would cause the main transformer breaker to trip on overload.
Best to have a qualified electrician or electrical eng review your plans.
Trends
Always a good idea to get a review by an expert. Some transformers can be overloaded depending on their insulation class and ambient temperature.