Tomcat or JBoss hosting 1 webapp with multiple websites

I want to have 3 websites, all with distinct public domain names but they all share a common java back-end SpringMVC server and use common static web resources like js and css files.

Rather than maintaining the UI code in 3 places, I'd rather run 1 server and deploy 1 WAR on a Tomcat8, Jboss or Wildfly cloud instance like OpenShift or AWS, but still be able configure my dns CNAME's to point to different paths on that WAR.

For example, here is where each domain would map to their respective endpoints but not have visibility of the others:

www.mydomainA.com ---> http://ift.tt/1OnuMi5
www.mydomainB.com ---> http://ift.tt/1GhGbGh
www.mydomainC.com ---> http://ift.tt/1OnuMi7

Is this possible? If so, what would be the steps to configure?