Repair a broken set screw in ball-type faucet

I was trying to repair to diverter on my kitchen's ball-type faucet, but I couldn't remove the bonnet. Knowing I need a better wrench, I put the handle back on, but the set screw busted while I was tightening it. Part of it is cracked. I was told I need a new handle, but I'm wondering if that's true. The set screw looks like it would normally come out if it weren't crusted into the handle. I figured with a Dremel I could work it out without much fuss. Do they make standard set screws that I could use instead? Am I wrong on my assumption that I could remove the set screw?
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you can drill it out and retap using a slightly bigger diameter screw.
figure in drill bit and tap new handle is cheaper
put anti seeze on allen in new handle to avoid a reoccurence
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The set screws are usually made of stronger material than the handle. Unless you are very skilled at drilling and tapping things, just throw it out and get a new one.

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Thanks everybody, I just got a new handle today.
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