I think Lilies under Tulips is a great idea. I already had this in mind with a patch of Lilies I put in the ground last year (usually I keep them in pots) and suddenly discovered an opening this spring that definitely says Tulip to me!
I am very interested in double planting although I don't have need of baskets for critter reasons or changing reasons although marking their locations is a great idea. I have lost a lot of daffs in my time by forgetting where they were, silly me.
Anyhow, I am going to try some perennial combinations through the summer for instance, my Oriental Poppy flop got planted with Cosmos last year but I would really like to discover a permanent arrangement with something rising through the Poppy foliage for later summer display.
I really will enjoy this learning curve in my severely lacking design skills. 
Sedum is definitely a plant to consider perennial double planting...and I have lots of that.