How do we implement a metamodel that is built on another metamodel (meta-metamodel) to support a domain specific framework for a healthcare system management?
Your metamodel will be based on the elements of the metametamodel.For example, you have an Ecore model that is your metametamodel, then your extend it to create your domain-specific language metamodel (such as Healthcare). This is your metamodel. As long as you instanciate the metamodel you have a healthcare model. Feel free to share an example of your advances, if you need more help.
For implementation you need some tooling that is capable for metamodeling and then instantiating that as a modeling language. A list of such tools is available at http://www.dsmforum.org/tools.html and there is also a number of industry cases listed at http://www.dsmforum.org/cases.html.
I know personally some cases on health care systems but on medical domain my hands-on experience is mostly related to medical devices. One public one is http://www.embedded.com/design/programming-languages-and-tools/4429401/1/Using-domain-specific-modeling-languages-for-medical-device-development
As said Cristiano, to create your metamodel, you should use EMF. You can use Ecore Tools to create it easily : https://www.eclipse.org/ecoretools/
Then, you can use Sirius to easily create your designers. They will relied directly on your metamodel and you are fully free to customize the behavior and the graphical style of each concept: http://eclipse.org/sirius/
All these projects are OpenSource and mature.
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