Based on
Alice in Chains: I highly recommend Drain STH, an all-female band out of Stockholm. Unfortunately, they only put out two albums in the late 1990s and then disbanded. Both albums are very good. The first,
Horror Wrestling is just a stripped-down, heavy, pissed-off-sounding awesomefest that sounds a lot like AIC's heavier stuff. Their second album,
Freaks Of Nature, is also very good, but is a bit different in that they added in a lot of loops and electronics. Good stuff all around.
Based on
Nightwish, I'd recommend Within Temptation and Epica, but I'm assuming you have already checked them out.
Based on
Pearl Jam, I highly recommend never listening to music again.
I assume you've checked out Soundgarden? How about Mother Love Bone, which was the original band that Pearl Jam and Soundgarden basically came from?