Tigertiffc,
Welcome to the forum! You have a great question. The answer is something of a gray area combined with a touch of 'doing the right thing.'
First, look at the shop instructions. Sometimes, they anticipate this situation and will answer the question, usually prohibiting multiple shops at the same time.
However, there are times that the shop instructions are not on point. In other words, they don't prohibit two shops at once. Then you must consider what you are providing for the MSP/client. That being the observations of a shopper based on the scenario they provide. If you add an unrelated event(s) to the shop, as you would by completing two shops at once, you would change the timings, add an unreported block of time to the narrative, or other things that might impact the observations. As such, it would be the right thing to do to complete only one shop at a time.
That being said, there is nothing to prohibit asking the scheduler(s) if you can do two at once. It is not unheard of to get permission to do so. If you want to read more comments I'm sure there is a thread or two out there on the subject.
Good luck!
Happily shopping Rhode Island and nearby Massachusetts and Connecticut