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Yes... you should definitely give it a try! The flavours will get enhanced too! Hope you will love the beets.
Perhaps you can gently steam them for 2-3 minutes to tender them and then add to the brine.

I keep on experimenting with various ingredients to get some amazing delicious outcomes.

I will definitely do that with the beets. I love them and have a great recipe for pickling them. The recipe is in this post:

https://hive.blog/hive-114308/@sunscape/recipes-for-preparing-mint-jelly-raspberry-jam-and-spicy-beetroot-by-sunscape