Is there media player with support of multiple genre tags
Solution 1:
None of the major media players (Windows Media Player, Winamp, etc.) has this feature, but I think MediaMonkey has support for multiple genres. Haven't tried it myself, but here is a screenshot I found:
To add multiple genre tags, separate each genre with a ';' (semicolon).
Update: It seems MusicBee is another player that has this feature. It can handle multiple artists and genres.
Solution 2:
Foobar2000 does have support for multiple genres. Separate the genres with a semicolon when editing tags, like this: "Punk; Rock". A track tagged that way will show up under both Punk and Rock genres.