'06 CTS 178k miles. Have changed batt several a times but continues to no start

I own a shop specializing in Cadillac and Corvette. Sounds to me as though there is likely an issue with starter, specifically the contacts within the starter solenoid or the wire connection at the starter solenoid. This is somewhat common due to the location of the starter and the location of the catalytic converter on the exhaust manifold. Of course it could be several other things as well. You are welcome to contact us at 727-430-8750 if you are still having issues. Russell with RB Auto Service.