Is one allergy shot containing multiple allergens as effective as many shots with one allergen per shot?

Yes, but: Yes, but the most essential component to giving allergy shots is that the appropriate doses are given for each allergen. In other words it doesn't matter if you get a certain number of units of dog mixed with a certain number of units of cat, or if you get those doses in separate injections. Also allergists know which allergens can or cannot be combined.

Yes but....: sometimes certain antigens/things can't be combined...and why get lots of shots when only a few suffice.... getting correctly identified as what you're allergic to and the safe escalation of SCIT shots is what matters.... or start sublingual immunotherapy (allergy therapy...it doesn't have to be just shots)