Lately I've been listening a lot to the music of the a cappella group Pentatonix. On the surface, their music is stylistically not the kind of thing I typically like - I very much prefer Bach, Ellington, and Yes to recent pop.
Yet their music, despite its pop roots, has a strongly progressive element: the arrangements are adventuresome, the center of musical focus changes throughout each song from one voice to another, each person in the group is a virtuoso, etc. I don't know if there's a genre of progressive a capella (progcapella?), but if not then they're founding it.
Reflecting on why I like Pentatonix has led me to think about the similarities between progressive music across different styles. Clearly my favorite band, Yes, is one of the greatest progressive rock groups. I also love the music of Hot Rize, which was a kind of progressive bluegrass outfit (currently reunited, albeit without their original and very progressive guitar player, Charles Sawtelle, who passed away some years ago). I'm a fan of progressive folk groups like Fairport Convention, Mellow Candle, and Steeleye Span. Going back further, the Duke Ellington Orchestra can be seen as a progressive swing band (compare their orchestrations and compositions to more conventional swing bands of the time).
To sample the more progressive side of Pentatonix, I'd recommend especially their songs "I Need Your Love" and "Daft Punk" (they're quite popular on YouTube so their videos are easy to find). While listening, keep in mind that they don't play any instruments - all the sounds are produced by the singers, including the crazy percussion and synthesizer sounds from beatboxer Kevin Olusola (for example at the two-minute mark of "Love Again").