Given the paradox of radical holism, we have the following option: either abandoning holism and finding a viable version of atomism (Fodor) or molecularism (Dummett, Perry, Marconi) or, on the other hand, keeping holism and abandoning the traditional view of communication as sharing common meanings or contents (Davidson, Brandom, Stalnaker). I will treat some of these solutions to hint at their limitations which seem to point towards an alternative: local holism.
The atomistic option has been taken by Fodor. A basic argument against any form of holism has been developed in Fodor-Lepore 1992. They claim that alternative options are almost impossible to accept without either falling into holism or accepting a principled analytic-synthetic distinction, which has been shown untenable by Quine. If you accept the idea that in order to communicate you need to share some belief you fall into holism, because there is no principled distinction which permits to decide which beliefs are the relevant ones (unless you accept a not welcome principled distinction between analytic and synthetic).
A way out is to accept that meanings are atomistic: each concept is an atom which is causally activated in our mind (in our innate language of thought). Authors like Fodor 1998 claim that the atomistic option is the only one which permits to overcome the problem of holism. The atomistic stance had received a strong theoretical support with the publication of Wittgenstein's Tractatus logico-philosophicus. However the logical atomism vivid in the early period of analytic philosophy received also strong criticism by most philosophers, including Wittgenstein himself. The new version of atomism given by Fodor seems a psychological adjustment of a already untenable position. Strange enough Fodor and Lepore accept the Quinean criticism of the analytic-synthetic distinction, forgetting that the main target of the criticism is the atomistic theory of language (the idea that sentences has a meaning in isolation from other sentences). The dismantling of the atomistic theory of language implies the dismantling of the idea of the atomistic theory of the meaning of single words (which had already been definitely destroyed by the results of structuralist linguistics). The new claims for atomism are more supported with the negative criticism of alternative options than with positive arguments. I will leave therefore the atomistic option as it is, to verify the robustness of the alternative options.