So you made a scheduling mistake and double booked yourself. No problem this happens to even the best of us. When you don't have a calendar in front of you there's always a chance you'll make a mistake.
Just call up one of the two company's (the one you're less interested in) and apologize that you'll need to reschedule because you've got another engagement you forgot about that you can't really change. (How honest you choose to be is up to you, but really just a decent apology should be enough)
With that done you're good, odds are this won't significantly impact your getting the job, if it does that's not a great sign for the potential hiring company being reasonable to work with.
DO NOT TRY TO JUGGLE TWO INTERVIEWS!
So yeah that TV episode (which has been done by probably a hundred times) always ends badly for the double booked individual. (because this is practically guaranteed to end badly from the start)
Let's say things line up perfectly and while one person's pitching you're responding to the other, us mortal meat bags despite thinking otherwise are REALLY BAD at multitasking with anything that requires more than a handful of brain cells. If you're talking to interviewer A you're missing half of what interviewer B says which will become obvious when they ask for feed back.
If things don't line up perfectly this will get even worse as you constantly will need to say, "One sec" or they're left with a long pause while you switch conversations.
At best you'll come across as disinterested, terrible at listening, or distracted. At worst you'll come across as just plain rude. Both of which means your resume and your chances of getting this job go straight into the trash can.