My department/school uses a specific software application for many users and I'm fairly sure several other departments/schools at UAB use it as well. Is there a more economical way to purchase that software

Possibly, through either a volume discount arrangement or through a site license.  First, contact AskIT to see if any discounts are already in place. If not you can send an email to dyother@uab.edu  for review. Make sure and included all pertinent information about the product such as areas known to be using the software, number of license currently owned, manufacturer, product name/version, etc., and why you feel a site license may be applicable.