Administratively, how can you purchase multiple licenses from the Mac App Store? I need to purchase 10 licenses for an app found on the Mac App Store (not iTunes). How do I go about purchasing those 10 distinct licenses and then deploy them to their respective machines?
Administratively, it might be easiest to use the gift feature to purchase all the 10 apps at once and file your expense reports. You are then free to use that account to redeem one copy - or pass off one (or more) of the redemption codes to whatever deploy accounts you use.

Currently, the iOS app store has more volume purchase options:


App Store Volume Purchase Program for Education
App Store Volume Purchase Program for Business 


I would join one of these if you can and inquire if/when it would extend to the Mac App Store for OS X. (Nothing speaks louder than action).

In the mean time, you can use gifting to separate the payment from the redemption and hand out the redemption codes as needed to the actual accounts you use to deploy the apps. I haven't had any issues with one account on 15 macs to ease the administrative burden. Do make sure to buy enough copies before adding new macs to keep things within the terms of the license. My reading (and I'm not a lawyer) is a person can install their apps on macs they control and own with no limit (not 5 or 10) and businesses/organizations are to buy one license per machine. I don't see a technical or moral reason to actually redeem each copy (especially if you secure / never further distribute those redemption codes). 

I personally can't wait until a unified volume plan arrives for the Mac App store - discount or not, having it centrally managed and downloading a spreadsheet to track things is so useful as we're more constrained with time and expertise than the cost of the software at present.