Does general Attack Speed Increase stack with Sword Attack Speed Increase? Like if I have GASI Max and SASI Max, does it do anything more than just one or the other?
Question on ASI
So, as what Bopp mentioned earlier, you can always check the abilities page where it states such UVs are capped at +6. But I'd like to give an example regarding your case.
If let's say you had a generic attack speed increase of +2, and you got a sword attack speed of +4, that would mean your sword's attack speed is +6, while your other non-sword weapons are +2. These don't stack further than the limit though, so if let's say your generic attack speed was +3 instead, your sword attack speed will still be +6 since that is the cap, even though not all of the 6 points were from sword attack speed.
I realised this with my Barbarous Thorn Blade. While it states that my sword dmg bonus is maximum(+6) and fiend dmg bonus is maximum(+6), that doesn't mean my sword dmg bonus is +12 against fiends and +6 against everything, it is just +6 against everything because that is the cap.
To add onto this, there's a few scenarios in which your attack speed can be pushed above the maximum, but they are always temporary buffs, not stat increases on the gear/weapon.
You can stack additional attack speed with a weapon after coming out of deadly shadow cloak, for example, which will go beyond the gear "maximum". However, this only lasts a few seconds before it's back on a cooldown.
This is all explained on the wiki page "Abilities". It includes detailed examples.
The short version is: All sources of ASI on a weapon add up, but there is a cap at +6.