Are there any awesome punk bands like Jane's Addiction with amazing harmonies like Queen?

Don't know but neither of those groups are punk.

Actually....most of the harmonies in QUEEN songs were done by Freddie. He had such uncanny precision that he did many of the harmonies overlapping each other by himself using his unique 3 octave range. It was usually just him and Roger singing. Brian's voice was usually too weak for harmony and of course John never sang. He just lipsync'd.

Check out a band called Tally Hall...they are awesome....and have some modern queen-esq sounding parts...you will love the song "Good Day"

Jane's addiction is not a punk band.

Try some old stuff like Ten Foot Pole or Lagwagon.