Cumbrae's and Healthy Butcher have both done so for me in the past. I just ask for medium ground, however. I haven't asked for specific cuts.
If you tell them they're willing to pay whatever the price is, I'm sure it will be ok - as long as you're not trying to bring your own meat (which I don't think you are). That would be a health and safety issue, and I don't think any Butcher will agree to grind meat that they aren't selling themselves.
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