IME it goes by the rules of the first carrier, but it's YMMV.
AA does allow 3 bags now if you are in Business or First on AA.
The problem was that there was no room in Business on the JFK-Toronto leg, but AA told me that the luggage allowance is based on the main flight - which was the Toronto-TLV, and they did allow me 70 lb per suitcase - but only 2 of them per person.
At least it was easier to shlep