David Lewis' modal realism is, in the author's opinion, one of the simplest and most useful theories of possible worlds. Nevertheless, it is not free of serious problems. In particular, important arguments against it have been endorsed by Forrest, Armstrong, and King. The answers to these arguments that were proposed either by Lewis himself or by other philosophers are not entirely satisfactory. Therefore, the aim of the present paper is to find better solutions. To provide them, an 'extension' of genuine modal realism is proposed. The crux of the 'extension' is to introduce higher-level modal operators, which can be used to incorporate into the theory provisos that make it possible to solve the apparent problems indicated by Forrest, Armstrong, and King. A semantical analysis of these 'meta-modalities' requires us to accept the existence of higher-level possible worlds. Apparently, this is in contradiction with one of the fundamental theses of Lewis' modal realism: all possible worlds are of the same kind as ours. But this is not so: higher-level possible worlds are just sets of zero-level worlds; ergo, there is no reason for not being able to talk about them.
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