The passive bi-amping you're inquiring about simply won't do that.
No, bi-amping will not provide better quality. Using the more powerful amp may improve things, if and only if you were exceeding the HK's limits to begin with. Since you have both already, go ahead and try the external JBL amp. At the least it will increase your available headroom a couple of decibels. Unless you were really taxing the HK, chances are you won't hear any difference with the outboard amp.
'Gaining more quality' as you put it usually starts with the speakers, and how they couple to your local acoustic environment, so start there. Get yourself a copy of Toole's latest edition, and put some of what you learn into practice, and you'll get more quality than bi-wiring could ever provide.