3500 tire sizes

Gentlemen, I have a 2003 3500 dually. Would like to replace worn tires with something taller in diameter. Currently have 195/60/15 Conti with an overall height of 26" Can this be done without effecting ABS, Trans and anything else important? I understand speedo will be off. If so how tall can I go without fenderwell mods? I have been to 2 tire stores and 2 dealers here in Mass and all just scratch their heads. Thanks for this info, Mike D.
 

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