If in the course of interacting with an external world, a person is creating a set of coherent knowledge about this world, then there should be a mapping between their beliefs and the external facts. In this case, surely something can be held to be true both through correspondence and coherence definitions?
I think the end answer is no. Or rather, any theory that is also a correspondence theory is going to be at its core a correspondence theory. The reason for this is subtle but relates to a generally unsaid feature implicit in the standard understanding and application of the term coherence theory of truth.
A correspondence theory is defined as
the view that truth is correspondence to, or with, a fact (SEP).
A coherency theory of truth conversely is defined as:
A coherence theory of truth states that the truth of any (true) proposition consists in its coherence with some specified set of propositions. (SEP)
On these simple definitions it sounds like one could maintain a view of truth that is the conjunction of these views (coherence + correspondence).
What is missing from the simple definitions is that coherence theory (as a view positively held under that name ) is a rejection of the correspondence theory. In other words to advocate the coherence theory is to reject that truth is about correspondence to a world fact (however parsed).
In other words, we could say coherence = the coherence thesis and the negation of the correspondence thesis. This would give us "truth of any (true) proposition consists merely in its coherence with some specified set of propositions"
Now, there's some historical backfilling in claiming views like Hegel are coherence theories. If we're calling Hegel a "coherence" theorist, then things are a bit muddier as to whether his view simultaneously declares that a proposition is true both insofar as it is coherent with the categories of our thought and insofar as it corresponds to the world.
In a broader sense, you could say many (if not all correspondence theories other than naive realism) include a coherence component. This is partially captured in questions about how we should treat universals. Insofar as we can consistently say "the light is red and the pen is red" we have to have a "coherent" definition of red.
Coherence theory is relativistic, holding ideas are cultural and being truthful is just being good at moving these concepts around. Correspondence theory is inherently realist at its core. If you want a view that incorporates cultural differences but still accepts that there are matters of fact, then you're not advocating a coherence theory by force of the definition. Instead, you'er advocating some nuanced correspondence view.
You could also believe there's facts (i.e. correspondence-possibility) in certain domains but not in others. Interestingly, this is basically the view the advocates who used the term "correspondence theory" under that name wound up with.
I will consider "true" a property of a propositions.
Then the correspondence definition of "true" reads:
A proposition is true if and only if it corresponds to a fact. This definition goes back to Aristotle.
A modern descendant is Tarski's definition: A proposition is true if and only if claims a fact.
Both types of definitions are faced with the problem to define what a fact is. And subsequently the question arises how to verify that the issue in question is a fact. The first definition in addition has to define the relation "to correspond".
On the other hand, the coherence definition operates only on the side of propositions. There is no need to take into account the domain of facts. Accordingly the coherence definition reads:
A proposition is true if and only if it coheres and is consistent with a system of propositions which has been accepted already.
Apparently the coherence definition is a relative definition, it defines "true relative to a set of proposition or better relative to an accepted theory."
One recognizes at once that the propositions, which a solipsist or a person in a state of psychosis accepts, satisfy the coherence definition of truth. But according to his fellow companions they do not satisfy the correspondence definition.
On the other hand, most people try to state propositions which satisfy both types of truth definition. Hence concerning many propositions many people consider compatible both types of definition.
I don't think so; unless you presume a lot of things such as existence (what is it?!) of an external world (that contains a lot of facts) and such as One's knowledge (and what is that?!) is obtained only by interacting with an external (presumed) world and so on...