Help with middle name

Caroline
We love the name Juliet for our baby girl. We were going to use the name Beatrix as a middle name (after my grandmother, Beatrice), but now I'm having second thoughts. I'd like for her middle name to at least start with a "B" or a "P" (after my other grandmother). 
What do you think? Stick with Beatrix (or Beatrice?) or choose another B or P name? 

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