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I've come across music that has a "G+7(♭9)". At first I thought this was just an odd way of writing G7(♭9), however there IS a G7(♭9) chord in the song as well. I feel that since they're named differently, they must have some distinction, but I don't know what.

I know of add9 chords, which are essentially 9th chords (1, 3, 5, 7, 9) without the 7th (1, 3, 5, 9). My best guess is that a +7 chord is a 7th chord without the 5th. Any help?

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You're almost there. The + here is not an alteration of the 7, but rather an alteration of the G triad that comes before it.

Thus G+7 indicates a G augmented triad (that's the +) with the seventh included. So you're looking at G B D♯ with an F included. If you also want the ♭9, that will be an A♭.

Edit: If you want my favorite use of this harmony, it comes in at 0:24 of the "Motherboy" theme from Arrested Development. In this case it's a C+7, but note that the raised fifth of the C triad slides up by half step into the third of the tonic F chord.

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    To me '+7' sounds even more dominant than a dominant, really needing to resolve. Can't give +7, but can give +1... – Tim Jan 18 '17 at 12:24

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