Thanks for the feedback. Is there any deliberation from philosophical point of view, any particular reference?

First all, you need to evaluate what's kind of theory you are working. For example, if you are using a formalized theory, it is so difficult to change the 'domain'. Formalized theories have a specific application. Second: when you change the "domain” you need to know if you are using the theory as an analogue for another problem. Analogues theories don't have the same force to explain diffrerent problems. Analogues could be more metaphoric than a proper explanation.

You could read ‘Aspects of scientific explanation” by Hempel. 

Yes, you should argue the case of why it might be relevant to the new domain first before testing in another domain. The relevance of domain- specific theory must be thoroughly explained as to How?, why?, what?, where?  who? and  which? to the knowledge of the untested domain. Generally, epistemology literature focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. Perhaps you could refer to:

Journal for General Philosophy of Science

ISSN: 0925-4560 (Print) 1572-8587 (Online) 

Thanks.

I think you should consider a kind of adaptation. you need to make that theory adapted to the new domain and perhaps make it operational to your research subject matter. More over, it is necessary to explain how and why the theory is relevant and proper for your research.

The question is sometimes (if not very extensively) addressed under the topic of "model transfer". As a primer, I would suggest to read the specific entry in the Stanford Encyclopedia of Philosophy under: http://plato.stanford.edu/entries/models-science/. If you want to go more thoroughly into the technical details, you have inevitably to deal with mathematical model theory, where any kind of mapping is based on purely formal logic.

Interesting question.  Given that knowledge is agreed on in the discourse (Kuhn's The Structure of Scientific Revolutions is one of a number of works highlighting this) and, as Paul Feyerabend says, whoever has the best argument has their material taken to be knowledge, (in Against Method). So you need a good argument for doing this.

The best argument is that by doing so you are showing something interesting and worth knowing. That would mean first showing the results of using that domain-specific theorum in a different domain.  Of course, if nothing new and interesting comes out of it, then there is no point in writing anything.  But of the results are new and interesting, then that is justification in itself.

Sometimes it is best to start the write-up with what you are doing, even if you have already completed it.  The results then back up your reasons for changing the domain of the theorum.  

Also, be prepared to adapt the theorum a little to the new situation.  The results may suggest this anyway.  Transfering approaches to a different domain frequently mean some adaptation to the theorum.

If I want to use a domain-specific theory to another domain where the it was not tested before, do I need to argue about domain-relevance first?

Yes, you should provide justification why that domain-specific theory is relevant in another domain which has no precedent / not tested before.  Because all our conceptual framework / research model needs to underpin on some theoretical frameworks /  theories / closest theory when there is no precedent theory being used in the particular research domain you are embarking on.  If this justification is not adequately provided, the adopted underpinning theory can be questioned during proposal defense or article reviews.  So better do the right things than doing the things right as the latter needs more costs / efforts to rectify.  The relevancy justification can be from your rigorous literature review (e.g. inclusive why no other researcher adopt your similar thinking etc), testing with other researchers or bouncing ideas with RG members like what you are doing.  Wishing you all the best.