Fillet or Boning Knife
Once you get in the habit of filleting your own fish or cutting up your own chicken, you’ll probably eventually want one of these. The super thin, narrow, flexible blade makes it easy to slip in between bones and joints in a way you just can’t do with a chef’s knife. Even if you’re not interested in boning your own fish or parting out a chicken, these knives are great for trimming the silver skin or excess fat from large cuts of meat, or trimming off thin skin from large fruits and veggies without forcing you to grab your (often shorter) paring knife.
You’ll probably have better control and leverage with a chef’s knife for those times you may be tempted to use a cleaver, and if you run into that many situations where a cleaver would be better.
A heavy cleaver is best so you don't damage your main-line knives when hacking up bone. A heavy cleaver is also heavy enough to use the back of the knife for cracking a coconut)
A Chinese cleaver designed for both chopping and delicate slicing (compared to a heavier European-style meat cleavers) can pull triple duty in your kitchen for vegetable chopping and dicing (once you know your way around with one, finely chopping even dense vegetables like cabbages and carrots is a breeze), an impromptu bench scraper, and hammering through bones and joints of large cuts of meat.
Kitchen shears (for snipping herbs without a cutting board or cutting the back out of a chicken). You’ll want a pair that can be easily washed, that come apart into two pieces (but not so easily they’ll fall apart while you use them), and are easy to handle and grip even when your hands are messy
Messermeister 8.5” Take Apart Shears if you like the design and need more leverage (although lefties may not like them very much.)