As a step towards resolving a question of Ru\v{s}kuc on the decidability of joint embedding for hereditary classes of permutations, which may be viewed as structures in a language of 2 linear orders, we show the corresponding problem is undecidable for hereditary classes of structures in a language of 3 linear orders. Comment: 20 pages. DMTCS version. arXiv admin note: substantial text overlap with arXiv:1903.11932