Resubmitting to multiple journals is not a typical (nor the "right" one however it is interpreted) strategy though (at least not in physical sciences). You'll usually ping the handling editor, who will then contact the referee on your behalf. The referee will then either "promise a report soon", or, in the event they didn't reply, the editor will find another referee. Nowadays with arxiv and such, there is usually no rush to actual publication as far as priority is concerned.

I'd also say, don't take the combative mindset as suggested in the comic. Think of it more as having some fresh pairs of eyes to check your work as well as communication (if a referee misunderstood something in your paper, chances are many readers will as well).