Whenever drawing from Multiple Vials into the same Syringe.
Draw from the 1st Vial, now get All the Air out, like you were getting ready to Inject it.
Now you can Draw from the Second Vial, without having to Inject Air into it.
When you are done with the Second Vial, again, get All the Air Out, like you are getting ready to Inject.
Now you can Draw from the 3rd Vial................................. JP
P.S.
I Personally have used this Method for many years, as it's common for me to Draw from 2 or 3 Different Vials.
Just make sure to Switch the Draw Needle for a New One, before Injecting.