There are a number of ways in which a single text could be said to have different meanings, and a number of them have come up in literary scholarship, rhetorical theory, and philosophy of literature.
(1) One way is polysemy in the proper sense: it belongs to the meaning of the text to be taken in more than one definite sense.
(2) Polysemy needs to be distinguished from mere ambiguity, however, although sharp distinctions are often not made in practice. Polysemy in the proper sense is conjunctive. If I write a double entendre, the whole point is that the same text has more than one definite sense, and this having-of-two-senses is itself part the meaning: the text means both. Mere ambiguity, on the other hand, is disjunctive. If I'm merely ambiguous between two senses, it is indeterminate what my meaning is: it could mean one or the other. We could call this polysemy, too, if we wanted -- and it often is called such -- but we do need sometimes to distinguish the conjunctive and disjunctive forms, because they function very differently in interpretation.
(3) Another way is polyvalence. Polyvalence occurs when the text, taken in one sense, admits of different valuations of that sense. As Celeste Michelle Condit puts it (talking in the context of television), polyvalence is "the fact that audiences routinely evaluate texts differently, assigning different values to different portions of a text and to the text itself." Thus if an author writes a text that is making use of polyvalence, he or she has carefully set up the text so that even if the readers agree on the meaning of the text in the narrow sense of what actually happens in the text, they can still disagree on the meaning of the text in the higher order sense of how to interpret this lower-level interpretation. For instance, you might have a story in which it was perfectly clear what a given character did, but where different people could take this same character doing this same thing as acting heroically or villainously. Or, for instance, you might have a story in which it is very clear what happens in a crucial scene, but the story itself leaves open whether the scene is merely a dream or a real part of the narrative. The ending of the Consolation of Philosophy is importantly polyvalent in the sense that we can read it either as Philosophy succeeding in curing the narrator (the traditional way of reading it) or as Philosophy failing and settling for the best she can do (which is what we find in the interpretations of Relihan, Marenbon, etc.).
(4) A fourth way texts can have different meanings comes from some of the excellent work of Scott R. Stroud on philosophical narrative: a text could be multivalent. As Stroud puts it: "A multivalent narrative uses contradiction and multiple value structures within the text to allow audience members to 'grasp' the familiar portions of the narrative and then slowly acculturate themselves to the non-native portions of the concepts involved through reconstructing what the narrative means in terms of valuation." Thus Krishna, to use Stroud's example, provides multiple arguments for Arjuna to fight, but they aren't all obviously consistent with each other -- they aren't necessarily inconsistent, but the text is building a situation in which we have a lot of different kinds of values involved, and their interrelations are partly left to the reader or listener to figure out. The Consolation of Philosophy also provides an example of this: there is a shift in the kind of argument being made between Book II and Book III, so that the terms and arguments of each are not exactly on a par -- in Book II we are dealing with preliminary approximations as Philosophy provides the weeping narrator painkillers, and in Book III we begin to get a more rigorous approach as Philosophy begins to shift from strengthening the patient to treating the underlying disease. In a multivalent text, we have different kinds of values side by side in the text itself, and their relation is not resolved, because part of what the text is doing is putting the question of how they relate to the reader or listener (and this even if the text overall gives guidelines to how the reader is to do it).
So are there other ways in which we can talk about texts having different meanings?
Quotation from Condit is from Celeste Michelle Condit, "The Rhetorical Limits of Polysemy," p. 498, as found in Contemporary Rhetorical Theory: A Reader, Lucaites, Condit, and Caudill, eds. The Guilford Press (New York: 1999).
Quotation from Stroud is from Scott R. Stroud, "Multivalent Narrative and Indian Philosophical Argument: Insights from the Bhagavad Gita," Journal of Indian Philosophy 7.1 (2002), p. 67. This is available online (PDF). He has other texts on the subjects, including "Narrative as Argument in Indian Philosophy: The Astavakra Gita as Multivalent Narrative" (available in PDF here) and "Multivalent Narrative: Extending the Narrative Paradigm with Insights from Ancient Indian Philosophical Texts" (available in PDF here).