Hello. Welcome to the forum and congrats on your guitar!
It all really depends on what types of sounds you're looking for. Are the big bands jazz bands? Are you looking for something that stays really clean, sounds really fat, breaks up when pushed or all of the above?
Most amps that aren't modeling amps can do one or two things really well and have their sound. Modeling amps seem to do most things ok, but nothing really well IMO. For example, a Blues Junior, Bassman, AC30, Marshall Plexi and Bose L1 all have the one or two things that they are known for and do really well. You'd never try to get a Blues Junior to sound like a Marshall Plexi. However, you might get a Line 6 to sound like a facsimile of either one.
A Yamaha acoustic modeling amp could cover a good amount of ground too. There are plenty of options like AER Compact 60 and 90, Acoustic Image Clarus with Raezer's Edge cabinets, Fender Jazz Master Ultralight, Polytone, Ultrasounds, Fishman SA220 or Loudboxes, Bose L1, Roland, Genz Benz, etc., BUT if you like the Acoustasonic and it works for you, I'm not sure that you need to look much further. Don't get me wrong, I love my Fishman Performer and know that it is the acoustic amp that I've been waiting for, but if you already have something that works for most of your situations, that very well could be your answer.