A number of railroads, particularly in the West, liked to use F-units instead of E-units for passenger service, but it wasn't possible to carry enough steam-generator water on them for a long trip, so EMD designed a lengthened version with an A1A rear truck: the original FL-9, which was never built. This is described in an article by Preston Cook in the July 2008 "Railfan and Railroad": strongly recommended, like all of Mr. Cook's historical articles!
When the New Haven needed units with both passenger equipment (including boiler water) and the extra equipment needed for third-rail operation, EMD used the five-axle FL-9 configuration they had already prepared for a long distance passenger locomotive. Thus all the FL-9 locomotives actually built (60 for the NYNH&H) were of the variant design.
I think the FL-9 carbody was also envisioned for a never-built "FG-9" locomotive with a free-piston gasifier and gas turbine power plant.
Fwiw: the basic F3/F7/F9 is 50 feet (and a few inches) long. The FP-7/FP-9 (a 4-axle variant lengthened to carry extra boiler water) was 4 feet longer. The FL-9 is four feet longer again.