Limiting publishing of a custom post type

I'm finding all the features of pro sites to be phenomenal.

I do, however, am trying to get something out of it that I can't figure out.

I have a plugin that delivers a custom post type and custom taxonomy.

I'd love to be able to limit how many items can be published for that particular CPT and its taxonomy. Is it possible? Maybe some sort of home-brew hack to accomplish this (understanding that updates will nix the hack)?

TIA