Firefox captures Alt+Shift, but Alt+Shift+" is set as a dead key for my layout.
I do some typing in other languages, so I've set up a custom keyboard layout with all the accented characters. I've set Alt+Shift+" as the dead key for the diaeresis (e.g., alt+shit+" i gives ï). They layout works system-wide, and I can use my other dead keys in Firefox, but not that one. It's not absolutely necessary, but it's pretty annoying.
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Some keyboard layouts like the "US International keyboard layout" can use the double quote (") as a dead key to add a diaeresis (I have a compose key on Linux), maybe that works better.