My humble answer to your question is YES. It is necessary to build the model on a particular theory in quantitative research. More than one theories can also be used to support your model (framework). You can find the positive and negative side of a relationship in the literature on a specific area, however, the model must be rooted in a theory.
Is it necessary to build framework on the basis of a specific theory in quantitative research? Or can we say that literature review is also a theoretical ground on which we can build our research?
Yes you need to build a conceptual framework or research model for your research which is underpinning on other theory, thoeris, theoretical frameworks that you'd literature reviewed.
Answering to your question, When designing research model you may either use a single theoretical background or use multiple theories integrating them in your model. If we discuss well recognized and heavily researched fields it is sometimes hard to find a research gap. Integrating different theoretical perspectives is sometimes beneficial and helps to generate intriguing theory. So, basically you can build your model on different theories, by but there should be some you are referring to, in any case. I strongly recommend searching for a theoretical Background for your model, but it does not necessarily have to be a single theoretical approach.
I am agree with above answers and mine also YES. Theory is the most import like a root so if you have found some work related to your model that will be good and you are allow to publish your work with the ground theory. Good Luck