Multi-prompt delimited continuations in terms of single-prompt delimited continuations
So, it turns out, the paper describing the construction I mentioned in the comments answers in the affirmative:


  Our technique of removing a dynamic prompt is rather general and thus can be used for the design of many other delimited control operators, which permit capturing the continuation up to an arbitrary (not necessarily the closest one) enclosing delimiter.  It becomes entirely up to the user which delimiters to skip and how the captured frames are to be composed or used separately.


If you look at their method, it seems like the idea would be to tag the H and HV values with tokens that specify the different prompts involved, and have the h and h' functions compare those tokens to decide what to do. This isn't terribly surprising, because the multi-prompt implementation I'm familiar with uses (representations of) stacks with frames tagged with the prompt, and their technique uses 'static' shift/reset (and macros) to hide explicit manipulation of the stack implementation of e.g. control/prompt, more or less.