Per D9.1:2012 (itis almost the same as Newjersey posted)
for Procedure Qualification
5.3.1 Base Metals.
"A change from one of the following base metal groups to another, or a change to a weld between dissimilar metals, requires separate qualification:
1- Carbon steel with 0.30 % max. carbon and 0.50 % max chromium
2- High strength, low alloy steels
3- Chromium and chromium-nickel stainless steels
4- Copper and copper alloys
5- Nickel and nickel alloys
6- Aluminum and aluminum alloys
7- Titanium and titanium alloys."
and 3.3.5
"A change in filler metal "F" number requires re-qualification (see Annex A, Table A.1"
It looks like all A5.9 fillers are F6, and your ASTM A240 would fall under item 3 above.
Strictly speaking, you could qualify your combination of base metals and filler with the ASTM A240 and 308LSi, and be within the code for almost any austenetic base and filler. You mention A240, which is fine, but there are about a jillion grades(alloys) that can be had in this spec. Same goes for the A5.9/F6 category, there are a ton of wires that fall under this category. Probably wouldnt be too hard to find a base/filler combo that meets code, but would fail miserably under welding/service conditions.