Is it possible to create a TeamCity parameter via the TeamCity API?

Hello, I would like to know if it's possible to add a new parameter to a build configuration via the TeamCity API. I'm not looking to set value for a parameter, but rather to create a parameter on the build configuration itself.

For example, on my build configuration named "Release Builds", I would like to add a parameter with the name "src_path_build_xyz" where the xyz is a variable value that's different for different builds like "src_path_build_1_0", "src_path_build_1_1" etc.