While a dwelling is required to have one egress door, a dwelling may have more than one egress door. The additional egress doors are not required to comply with the minimum dimensions however, the other code requirements for doors apply. One of the requirements is that the door open without special effort.
This interpretation is probably going to get crapped on by the forum members because the code says "other" doors, as in not an egress door. That's okay, sometimes it takes an avant-garde approach to achieve an equitable outcome. Tell that to the contractor.
R311.2 Egress door. Not less than one egress door shall be provided for each dwelling unit. The egress door shall be side-hinged, and shall provide a clear width of not less than 32 inches where measured between the face of the door and the stop, with the door open 90 degrees. The clear height of the door opening shall be not less than 78 inches in height measured from the top of the threshold to the bottom of the stop. Other doors shall not be required to comply with these minimum dimensions. Egress doors shall be readily openable from inside the dwelling without the use of a key or special knowledge or effort.
The last sentence contains egress doors ... plural for doors ... more than one egress door which is an "other" door. So to you naysayers I say, there's a door sealed shut with Great Stuff ... who's willing to walk away from that?