Triple Irish Chain is one of my favorites. I actually completed one:
http://www.quiltingboard.com/members...237-292758.JPG
This pattern looks great when you have contrast. For a Double Irish Chain, maybe select one of the purples that you can't live without and find a coordinated white with purple print to match. For Triple, I would suggest adding a non-purple.
If you are sold on using all of the purples, maybe try a Trip Around the World, again adding some contrast with a coordinated white/purple print:
http://www.quiltingboard.com/members...237-286473.JPG
Please share when you make your decision and happy quilting!