Writing a Concept Test

So I have a series of concepts for a redesign of part of the product I work on. 4 concepts total. I want to test each one to decide on an overall direction for the redesign so that it's based on user feedback and not anyone's opinion or gut. But I'm not sure the best way to write the test so that I'm getting helpful feedback. The more I think about it, the more it seems like I can't just have 4 separate groups use one concept and give feedback on that one concept. I don't feel like I'll get anything definitive from that because they have nothing to compare it to.

Some other test set-up ideas I've had:

I could have one larger group use each of the concepts and choose which one they liked best through survey style feedback.

Or I could have 4 groups try the current design and then one redesign concept and give feedback.

Has anyone tested this way before? Any insight into what got you the best feedback?