This is an adjective that describes a single entity as comprising more than one component, as in the following established usages:

A multiple pregnancy involves more than one fetus.
A multiple circuit contains a number of parallel conductors.
A multiple star is a system of stars in close proximity, giving the appearance of a single star.
A multiple personality comprises several distinct characters.
In contrast, as illustrated in the last of the foregoing examples, several is a quantifier meaning more than one. It is unsurprising that the distinction is ignored by the editors of Webster's 3rd, who were so diligent in reporting linguistic atrocities and so remiss in identifying them, and in this case were moved to include several as a synonym for multiple, citing several (?) examples of this misusage. But is this a matter of such profound subtlety as to exceed the grasp of the vast majority of English speakers?

The educable exception may be instructed by the observation that multiple is a generalization of double, triple, etc. We do not speak of the quadruple seasons of the year; why, then, a product of multiple factors? Nor do we refer to the double plays that ended the top of the fourth inning; is it less absurd to say that a person exhibits multiple personalities?

The error may be avoided by limiting the use of multiple to the modification of singular nouns, but this is too restrictive, as we may sensibly refer, for example, to a group of women who are laden with multiple pregnancies. The rule to be followed is simply this: When multiple is used to modify a plural, it should be similarly applicable to the singular. If it is not, then several should probably be used instead.

No one has embraced this barbarism more enthusiastically than my colleagues in the computer industry. * I frequently hear of multiple possible explanations of a phenomenon, or even that an event has occurred multiple times. The Association for Computing Machinery has sponsored an International Workshop on Multiple Perspectives in Software Development, possibly the first symposium ever to be dedicated to the propagation of a single grammatical error. I quote from two articles selected at random from the proceedings:

The design of complex artifacts typically involves multiple designers sharing parts of an evolving design, sharing multiple design notations and tools.
-- J.C. Grundy, J.G. Hosking, W.B. Mugridge, and R.W. Amor, Support for Constructing Environments with Multiple Views.
... any project involving legacy systems, multiple organizations, multiple contracts and high volumes of variable quality documentation. In my experience, that means any large project.''
--G. Mullery, Tool Support for Multiple Viewpoints.
It would be misleading, however, to suggest that such abuse is confined to any particular demographic segment. In fact, it is so common that it is remarkable that I have not seen it challenged elsewhere. Especially disturbing are the occurrences found in the writing of those from whom I might have hoped for such objection, which I have occasionally brought to their authors' attention. The only solace that I have found to date was offered by Stanley Fish in a terse response to my plea: "You're right." A more typical reaction came from Bill Walsh, who admitted that he was unaware of any such controversy. "My instinct," he noted, "would be to file this under 'useful evolution,' as I do the use of 'gender' to mean 'sex,' [see GENDER] but to exercise caution when there's a possibility of confusion, as with 'multiple pregnancies.'" * While the evolution is hardly useful, the analogy is sound: the power of the language can only be diminished by the conflation of two words that previously served distinct and useful functions.

Finally, I consulted Geoffrey Pullum, not with any expectation that he might share my position, but rather because he usually has something interesting to say. Pullum's observation was that multiple is not the first adjective to be forced to double as a "determinative" (his word, in the strict sense that he and Rodney Huddleston seem to have invented it), little and various being other examples. Although Geoff's intention was to reassure me ("It is OK. No harm is done. Things will be all right."), his response had quite the opposite effect.

It is true that little has survived as an adjective in spite of its double meaning, but this word has the advantage that its two senses are generally distinguishable: adjective or determinative depending on whether it is attached to a mass or a countable noun. The rare instances that are open to both mass and individuated interpretations, e.g., Mary had a little lamb [and washed it down with a little milk?], can generally be resolved according to context.

The new meaning of multiple, on the other hand, like that of various, generates confusion. There was a time when one could write, for example, Various writers and artists were common during the Renaissance, using the adjective without ambiguity, but not today. Similarly, one can no longer refer to multiple stars or circuits, intending the original meaning of the word, without fear of being misunderstood. As an adjective, various is now all but obsolete; multiple is not far behind.