Boil all three types of rice separately in plenty of boiling water. The basmati will take 8–10 minutes and the others more like 20–30 minutes. Watch and top up with water to be sure the grains don’t stick together. When they are done, drain each pot of rice in a colander and rinse briefly with cold water.
Combine the dressing ingredients in a large deep bowl. Add the still-warm rice and toss to combine. Taste. You might want to add more salt or pepper.
When the rice mixture has cooled, add all the other ingredients and toss lightly to combine.
Garnish with blanched mange touts.