You would not need to increase the height in the whole roof section would you..?? If you could lift enough to get just enough space for the car lower window line upwards, you would not need to lift the whole section of the garage, just the section above the ramp and car roof section.
Nikos,
In the UK we have to put the foundations on bedrock, these can be at whatever depth is required, usually about 1 metre, Digging down and making a pit is an option, but I used to have one of these and unless it is fully lined you can get water ingress, so you would have to put in a drain below the 1m level, sufficient to drain off. Anything can be done but at what price is the question..??