Wet food switching

I thought I read somewhere that it's ok to switch up wet food brands/flavors often without the mixing/adjustment period that you have to do with dry food. I'm wondering if this is true. We get 3 brands of cat food (wellness, innova, merriks) in a variety of flavors each month and give them half a can each night (so they get the same can 2 nights in a row), in addition to their dry food. They've been fine on this for the past couple weeks but this week poor Phoebe has thrown up twice (however, she does have a history of throwing up, and has bad allergies) and I wanted to make sure the wet food switching wasn't causing this.
TIA!

Thanks, yeah, we mix in Natural Balance when the feed store has it but they're not always stocked. We'll check around the apartment and see if there's anything obvious triggering the allerigies. She normally throws up about once a week but it's been more frequent this week, but it could also be her eating too fast again.

I would check all of them for a common ingrediant like chicken or flaxseed