Can we purchase Build Configurations without purchasing Build Agent licenses? Follow

No, Build Configurations can only be purchased as part of a Build Agent license.

The Enterprise edition has no limit on the number of build configurations.

The Professional edition allows 100 build configurations per server since TeamCity 2017.2 (20 in earlier versions). Since TeamCity 8.0, each build agent license key gives you 10 more build configurations in Professional edition in addition to one more agent. All build configurations are counted (i.e. including those in archived projects).