I have a 2009 Giant Trance X1. Can I increase my rear travel to 140mm as currently only have 127mm.

Fit a 190mm x 50mm shock. Then fit a 3mm offset bush to the top eylet to bring the shock closely back down to orignal i-2-i that should add a bit extra travel without too much bother

Out of interest what extra do you think you’ll be able to do with an added 13mm of travel that you can’t do now? It may be a better idea to sell your Giant frame and replace it with something designed with more travel if you feel thats what you need.

Wouldn’t it steepen the head angle?

Wouldn’t it steepen the head angle?

Well, you’d have to (effectively) move the back wheel downwards, lifting the bottom bracket (shortening the bike slightly?) and steeping the head angle. So, yes. And it could well ruin the handling too.