Presuming you want to do this for security reasons because the POST message body would contain sensitive information. 

HTTPS encrypts query strings during transit but URLs can be recorded unencrypted within the receiving end's access logs.

Would the POST message body consist of query string parameters and, if so, would the names and number pf parameters be the same each time the message is sent?

Or can the POST message be JSON?

I have never tried this and will not guarantee it will actually work.

You can launch a window using "Open URL in Window". If you do not use alternative domain, the launched window can display a Pega Harness that references a Section. That Section can access a Data Page that contains an alternate domain URL, plus the information needed for a POST request. The Data Page can source an Activity. The Activity can create an "Interface" step page using the aforementioned information. Specifically that information is used to populate the QueryString or JSON text message body of an HTTP connector's POST request. The response from the POST request would be HTML. The Activity could then call Show-Stream to output that response HTML to the Harness.

1.Thing is One Application Opening another Pega Application means- Going to create new Session for launching the Application. This also to be noted

2. Along with the Request POST need to send neccessary information in form of Request Headers

Can be implemented making use of above considerations

Federated Case Management

https://community.pega.com/knowledgebase/understanding-federated-case-management

Federated Case Management (FCM) enables you to connect PRPC applications. Users in a federation (a group of applications connected by FCM) work in their local application portal, which can display cases and assignments from other applications in the federation. Each local application processes and maintains its own cases and data, and publishes data to a centralized database, the Federated Case Management Repository (FCMR).