According to AOL, Shake Shack is adding permanently to its menu a veggie burger and nondairy shake. See https://www.aol.com/finance/shake-shack-leans-veggie-burgers-120041981.html
Shake Shack says on their website:
We have a few options for Vegetarians and Vegans!
-Our new Veggie Shack is a meatless patty packed with veggies and topped with American Cheese, crispy onions, pickles, and ShackSauce! Make it Vegan by removing the Cheese, ShackSauce, and Crispy Fried onions, and requesting a lettuce wrap or gluten-free bun.
-Our Non-Dairy Chocolate Custard or Shake is made with creamy plant-based non-dairy frozen custard made with NotMilk™
-Our Fries are also Vegetarian and Vegan friendly!
See https://shakeshack.com/faq?a=What-vegetarian-or-vegan-options-do-you-have—id–BjalMAUDQDiC1tE9cMJgHQ