Can more than one semicolon be used in a row?

I teach writing and a student asked me an interesting question today which I have never considered. They wondered if they could use multiple semicolons one after another. That is, if they have a series of independent clauses that are closely related, could they use semicolons to connect them? As a native speaker I want to say this feels wrong but I can't find any reference to support my position. Does anyone happen to know the official rule for this?