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While there are loads and loads of bands with a pair of brothers in them — The Kinks, Oasis, Rank and File, Screaming Trees, Sedan Delivery — it’s much rarer to have a band with three or more brothers where they’re not the entire band.
Off the top of my head, I can think of two, both based in Southern California. The Beach Boys, of course, and the far less famous Pop Art. (UPDATE: I found another one! Turns out that the first two Bachman-Turner Overdrive album featured three Bachmans: Randy, Rob and Tim.) Consisting of singer David Steinhart, his brothers Jeff and Rich on guitars and a couple of other guys as the rhythm section, Pop Art some pretty great records of majestic jangle-pop, and even started their own label to release those records.