This is a great and complex matter. There are a few philosophers of art who come close to an "anything goes" approach to the meaning of a work of literature, but most of us think there are some boundaries in terms of historical context, the intentions of the artists, and most importantly the content of the work of art itself. You might consider a distinction that some find useful between the meaning of a work of art and the significance of a work of art. In terms of significance, a work of literature might have all sorts of features depending on how the work is experienced. Reading Jane Austin might lead me to become a Marxist and someone else to become a Hindu, and so on, but while the book could have such multiple, different significant effects, to get at the meaning of her work we would need to study the plot, characters, England and continental Europe at the time, the English style she used, and so on.... Once we take those factors into account we can see (or I wager we will see) that her work was not meant as Marxist or Hindu literature. Part of this seems to be the sort of thing we can debate objectively (pointing out that Austin died in 1817 whereas Marx wasn't born until 1818, for example) but we might also see how the meaning of a work might contribute to the significant future multiple readings and re-readings of works of literature. In this sense, the meaning of a work such as Sense and Sensibility might remain constant through your life, and yet the work had a radically different significance for you when a young reader than when you re-read it at sixty. I discuss some of these issues in a recent book, Aesthetics: A Beginner's Guide, which you may (or may not!) find of interest. You have certainly raised a central matter that requires far more of a response than I have attempted in this short reply. Good wishes.
Read another response by Charles Taliaferro
Read another response about Literature
If every person can interpret a work of literature differently, by linking the depictions with experiences in their life or knowledge they have acquired, how is it possible for literary critics to "analyze" the meanings of works of literature?