The assignment book for the Bronx in 1900 had five lines, but only was filled in for three alarms, and in some cases only two alarms.
In 1922 the National Board of Fire Underwriters recommended that the Chicago Fire Department increase the running assignments from three to five alarms and to include automatic change of quarters, The first five alarm cards were issued in November. 1927 for the downtown area. The entire city would not be completed until 1941. Also, from 1922, every engine, truck, squad, and battalion chief were given "still alarm" districts.
As far as I know, CFD running cards are unique in that the order of assignment is numerical and not geographic for each alarm.