For non-rated pairs of doors, there is no specific code requirement for a maximum meeting edge clearance. The end user or architect may approve clearances greater than 3/16”, but should consider the effect on security and appearance.
For rated openings, the 3/16” meeting edge clearance is measured from the “pull” or “wide” side of beveled doors. The 3/16” is the maximum clearance allowed per NFPA 80, regardless of the use of a flat bar astragal. Listed wrap-around metal edges may be an option and should be installed in accordance with the edge or door manufacturer’s listing.
The meeting edge clearance between double egress pairs of doors, measured from one side only, may potentially exceed 3/16” since the measurement would be from the “pull” side of one door to the “push” side of the other door. In this case, an allowance should be made for the degree of bevel.