Greater magic weapon / Bane ability

[GoldEdition42]

Due to the meagreness of cash (and spending most of our adventure in the wilderness) my 8th level Inquisitor merely has a MW Falchion for his main weapon.

Question: If I cast Greater Magic Weapon it becomes a +2 falchion for 8 hours, yes? I can also throw Keen Edge for 80 minutes of 15-20 threat ranger.

Ok, now I have to wonder if Bane's +2 stacks with the +2 from the GMW spell? I know it won't have a true +4 weapon's ability to overcome DR/Adamantine, but will it still give +4 to hit and damage?

Seems like it should.

Thanks.

[Diego Rossi]

Greater magic weapon give an enhancement to the weapon.
The bane ability add to a weapon enhancement.
They stack.