Potts' book has gone a long way toward revitalizing interest in conventional implicatures. One question the existence of such semantic characteristics raises is whether or not conventional implicatures (like other aspects of conventional meaning) can themselves license conversational implicatures. The answer, I submit, is "yes".
According to Potts, conventional implicatures based on expressives are always subject-oriented. By and large he seems right about this. However, there are cases which appear to exploit this fact in order to produce a double implicature: first a conventional implicature to the effect that the speaker has a certain attitude and then a conversational implicature to the effect that some other person (not the speaker) has this attitude.
Consider, for example, a situation in which a southern woman whose father is very "pro-confederate" is inviting her fiance down for the holidays to meet her parents. A friend overhears them discussing the potential upcoming confrontations and asks what the issue is. The woman responds, "Well, us southerners won't stand for no damn Yankees sleeping under our roof."
In this case, the conventional implicature is that the woman doesn't look favorably upon people from the northern US. But the audience is well aware that the woman doesn't have any such attitude. Since she has committed herself for something that is plainly false, the audience casts around for an alternative and hits upon the idea that the woman's parents don't look favorably upon Yankees.
I suspect this is too simple an analysis and other, more clever, folks can come up with better examples. However, supposing that such cases can be discovered, it raises an important question: Can Grice's principles reasonably cover this type of conversational implicature? There is some doubt. After all, Grice's principles are typically stated in terms of discourse cooperation and conversational direction. But since CIs are backgrounded, it may be possible to generate examples which aren't naturally covered by Grice. (The above example doesn't seem to do this since it might well be covered by flouting the convention of informativeness.)