Execution of multiple goals from the CLI is now supported in Maven 3.3.1+
mvn exec:java@first-cli
mvn exec:java@second-cli
Where first-cli/second-cli are the execution ids.
https://blog.soebes.de/blog/2015/03/17/apache-maven-3-dot-3-1-features/
For your example the commands would be
mvn myplugin:mygoal@process-cats
mvn myplugin:mygoal@process-dogs