Rezoning from Single Family to Duplex

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How difficult is it to get a single family lot rezoned to R-2 (or whatever code the locality uses for duplexes--it's R-2 in the area I'm looking at)?

I'm just guessing it is probably virtually impossible.  The whole point of zoning is to prevent the place from becoming a ghetto, so if they let people just change the zone at will it would be pointless.  However, I still hold out a slim chance it could be possible.