The term for parasitoids that attack other parasitoids is a "hyperparasitoid". I did my PhD on parasitoids that attack aphids, but I've never heard of a hyper-hyperparasitoid, do you have any reference to that example?
The caterpillar: Often a pest species like the tomato leafminer
Primary parasitoid: Cotesia glomerata
Secondary parasitoid: Lysibia nana and some species from the genus Gelis like agilis
Tertiary parasitoid: Certain species within the Trichogramma or Eulophidae families.