Sure! A build configuration can include multiple steps. While the build is running TeamCity displays it in the status for the build. If some step in the middle of the sequence fails, you will see the corresponding message in the build overview with a link that takes you to the correct place in the build log so you can investigate what happened.
What you are probably looking for is the ability to connect multiple build configurations into a build chain. In TeamCity you can configure a build configuration to depend on the other build configuration. See snapshot dependencies: https://www.jetbrains.com/help/teamcity/snapshot-dependencies.html