are you planning to add an opportunity to start a process model on different object-types like in an action? An Action is fine, but there is no start dialog, as in a process model.
The currently possible solution is to use the individual activity actions of type 'Link'. This allows to open another web-app. The process ID and activity ID are appended as URL parameters. So the web-app can do what required. See the documentation here.
Further currently discussed solution without concrete planning are:
What do you want to implement? It sounds like you want start a sub process. In that case you have the possibility to start a process in a serverside bpm event. For example WORKITEM_COMPLETE. You have to add the parameter to the sub process that you want. Either you already have these information or you have to put in on your form before. After forwarding the previous task, the event script starts a sub process. You find documentation about that on help.enaio.com. Take a look into server side bpm scripting and the rest-api of dms-service.