The 1906 Brooklyn City Directory (Upington's General Directory) may be on Ancestry, but I've never seen it; I don't think Ancestry has Upington's. I found it on Internet Archive. When I found Michael Mulcahy listed, there was a bit of a surprise. His home address is 85 Luquer, and his business address ("liquors") is 227 Hamilton - but also 291 Van Brunt! Michael Mulcahy owned 2 bars? I never knew!
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Then I went to Google Books and the Report of the State Commissioner of Excise. In the volume for 1910, 291 Van Brunt is listed under Michael Mulcahey. (Earlier volumes don't appear to list certificate holders.)
But in the volume for 1912, 291 Van Brunt was listed with James Mulcahy as the certificate holder.
Now, Michael had both a brother and a son named James. I don't know anything about his brother, but I know that his son James A. was born around 1892, which means that by 1912, he was about 20. Had he taken over his father's bar by that age?
I've heard a couple of stories about how the family stopped running the bar. A cousin I met doing genealogy says she was told that the bar on Hamilton Ave. was torn down to make way for the Midtown Tunnel. I don't know about that, but I know that 227 Hamilton is positioned to have very easily been in the way of either the Gowanus Expressway or the BQE. I'll have to look into the history of those roads, but I wonder if maybe the family moved the bar to 291 Van Brunt when the building at 227 Hamilton was destroyed.
A brief, unsourced family history I was given included the assertion that the family lost the bar after they changed the beer. And, in news that's perhaps related to James taking over the bar, I was once told that the family lost the bar when the kids took over, because they, unlike their father, didn't have the personality necessary for tending bar.
By 1913, a Frank Mulvihill held the certificate for the bar at 291 Van Brunt.