Not really, the hours and equipment you need to fix them properly all but makes it impossible. Shimano don't tend to have spares for STIs either. Don't think shifter repairs are part of their business model either, it certainly wasn't something you could be trained in when I was shop spannering. (Or team spannering!)
It's cheaper to buy a new one.
Tho I did once turn two broken shifters into one functional shifter. At workshop rates in the shop I was working at it would have cost around £200-225 for the labour. If the shop had been open at the time, I'd probably have been sacked for swearing.........