What I propose is that similarity sometimes plays no part at all, and that whether it does also varies with sentence and context. When it plays no part, the truth of the counterfactual in question requires that all A-worlds are C-worlds. (To state the modified theory elegantly, we could speak of 'all relevant A-worlds', defining 'relevant' using 'most similar' but adding that sometimes all A-worlds will be relevant.)
The argument for this modification involves what could be called categorical counterfactuals. Consider the following sentence, uttered in the context of teaching someone how to use the word 'bachelor':
(A) If I had spoken to a bachelor this morning, I would have spoken to an unmarried man this morning.
Intuitively, the truth of this hinges on the fact that bachelors are necessarily unmarried men. Lewis's analysis, without my proposed modification, although it gives the right truth-value, gives the wrong truth-condition and thus distorts the meaning of (A); it is false to say that the truth-condition for this sentence is that all the most similar A-worlds are C-worlds - on any understanding of similarity.
The modified theory handles (A) much better: this is one of those cases where similarity plays no part, and so (A) is true iff all worlds where I spoke to a bachelor this morning are worlds where I spoke to an unmarried man this morning. This seems right.
(A note on the structure of Lewis's theory as formally developed with systems of spheres: this can remain as is, but in the case of categorical counterfactual conditionals the “innermost” sphere will contain all worlds, and so it would be misleading to call the worlds in this sphere 'the most similar A-worlds'.)
Lewis, D. 1973. Counterfactuals. Basil Blackwell: Oxford.