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A car model, so the McLaren MP4-17 is a valid answer but not the correct one. In fact, there have been other McLarens with more starts than the MP4-17, perhaps most notably the MP4/1 and M23.McLaren MP4-17? In various iterations - A through to D - it made 66 starts in 33 races in 2002 and 2003.
Or do you mean an individual car, and want a chassis number or somesuch? In which case I have no idea.