Applying Dremel to a stuck kitchen faucet cap

I had posted before about a faucet cap I have and how to get it off so I can get to the diverter in my ball-type faucet. There was some speculation that it wouldn't come off, but my model looks like the cap is its own part with its own removal. I can't get it off. I tried liquid wrench along with whacking it with a hammer, along with trying to lightly chisel in underneath to loosen the grime. Finally, I warmed up the faucet with hot water for a minute. No go. I think I must remove it the hard way.
I've heard of some folks cutting them off, but there are problems with the threading. Has anybody here done this before? I was going to get a new cap and do this at a time of day when I can get a replacement faucet still--just in case. I figured lightly going at it with some metal cutoff wheels on my Dremel should get a cut into it without destroying the threading. It would be a different story if I press too hard on it. How strong is chrome/chrome-plated faucet parts against a Dremel?
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Why don't you just buy another faucet? That's what you'll end up doing anyway.

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I used a Dremel tool on a three-handled shower faucet. Darn thing was stuck for years. I'd say it was daring, but if the new stems didn't fit I would need to open the wall. If it's a Kitchen sink, don't bother unless it's fairly new.

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what brand model faucet? you might find repair blowup at mfr website.
i've done similar repair to an early 90's american standard ceramic cart faucet.
the instructions were a bit vague, said something like, "remove" cap. wow. that was informative.
i tried a strap wrench, which slightly crushed a less visible location, but didn't "remove" the cover. then i realized it would loosen (then come off) when i pried upward with a bit of effort.
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