Interpreting a text always involves a manner of interpreting. The manner of an interpretation informs how the material interpreted is organized, as well as what material is included or excluded from the interpretation. Depending on what is being interpreted, and why, different strategies may be employed. In reading to get 'the gist' most material will be excluded from the interpretation; in performing a detailed textual analysis, certain qualities (such as, alliteration, use of large or short words, &c) will be included in the interpretation; when reading for pleasure there may be more openness to reaction. These and many other ways of interpreting are familiar to us. I want to convey what it is to interpret in a philosophical manner.
Just as we may read Plato to get the 'gist' or Aristotle's Topics for enjoyment, interpreting philosophically is not restricted to 'philosophical texts'. Just like other manners of interpretation, sometimes it feels more natural and other times it does not. Most works considered 'philosophical' are good candidates, but also a large amount of poetry, fiction and scientific works. I will restrict myself here to more paradigmatic cases.
The primary characteristic of philosophical work, and so a quality of typical candidates for philosophical interpretation, is that ideas employed in order to understand something are being evaluated or first established. In these cases there is something being conveyed that will help guide the interpreter in understanding a great number (and often all) things that fall within the domain considered. For example, with Kant's Critique of Pure Reason, we can understand human experience of existences in terms of its limits, basic elements and structures. Just as philosophy works in evaluating and establishing ideas by which we think, philosophical interpretation also does this.
When interpreting philosophically one attempts to ground the ideas presented in it positively, that is, the interpreter strives to be able to navigate the domain the ideas present. In order to do this effectively, it is not enough to repeat the manner in which the ideas were set out, but rather to use the exposition of the ideas to guide an original undertaking in drawing the ideas out of the interpreter.
In the Mediations on First Philosophy, Descartes doubts his opinions, knowledge and experience of the world. In order to interpret Descartes philosophically, it is not sufficient to simply take what seems to be his conclusion - that the only thing we cannot doubt is ourselves, and when we consider what else we know from this, we also find that we know God best of all. Nor is it sufficient to go through some procedure of doubt that we understand, and then come to some conclusion - that I cannot doubt myself, but I can doubt the existence of God. Not even following Descartes' procedure and attaining the same result is sufficient for philosophical interpretation. What is called for is an original grounding of Descartes' thought which results in a new understanding of his procedure and results.
Through bringing about an original ground in the interpretation, one authenticates what is being interpreted, and can fully integrate it into their own understanding without any conflicts. This means philosophical interpretation is not concerned with agreeing or disagreeing with what is being interpreted. Instead, philosophical interpretation is a practice in thinking and understanding that cannot be attained in interpretations the stop at agreement or disagreement.
Such an interpretive procedure may be thought to efface the text interpreted. If I come to some new way of thinking Descartes' position so that I can also maintain it, then am I not just reading into Descartes in order to smooth out difficulties? No. If we can suppose that Descartes really did maintain the view that he wrote about, coming into possession of the capacity to understand that view, even if we also uncover its limits, is not "reading into" Descartes, but understanding what was left unsaid.
No philosopher can convey the understanding of their thought directly, but can only do their best to convey their thought in the hope that it will be understood. Because of this, every philosophical interpretation cannot be expressed without itself becoming another philosophical system that can only hope to be understood philosophically which means understood better.
Even if a philosopher has attained to completeness in their system to the extent that any interpretation will not prove it to be limited, the system itself will still not have encapsulated the understanding of itself; it is still up to the interpreter to attain an understanding, and a philosophical understanding makes what is understood its own, and recognizes the need to do so continuously.
What value does philosophical interpretation have? One may suggest a number of things, but they would all point in the wrong direction. There is no specific value to philosophical interpretation, since it may ultimately demand re-integrating and grounding any of these values. As Plato said, philosophy begins in wonder, and so does philosophical interpretation. This wonder should be thought of as an experience that frees us for thinking - not one that already has a determined and expected result - and which calls on us to enter into our interpreting philosophically.