You can use "charlieplexing" with '595 function (not pin) compatible TPIC6C595 or STPIC6C595
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or
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with a drive capability of 100mA per pin (250mA peak).
If you want to mux only 2,4 or 6 lines use 74LVC2G79 which can drive up to
50mA per output. The second register of the '595 is not really needed for your application.
MIKE