"How does a single owner manage multiple businesses at once?"
Start by understanding why someone has multiple businesses.
For some, a second or third business creates the opportunity to adopt new challenges as their existing successful business does not seem challenging.
Others see having multiple businesses as a means to "hedge your bets." The presumption lies in mitigating risk by adopting multiple revenue streams simultaneously.
And herein lies the problem many people face today.
If someone has no confidence in the success of a business, then find out why first. This answer provides insight into a less than ideal business or perhaps into someone's insecurities about their ability to execute - which is fine. Explore that. Assess where you feel you lack the knowledge or the experience to execute and go learn it.
If someone can't build one successful business, does it make sense to start a second before they learn why? If they can't fix the business, why still have it?
Now assuming you have a successful business and wish to run a second, this requires that either:
everything is either 100% automated, self-serve and with no customer questions
this means you need to trust people.
If it were me, I would find the right people to place in running the parts of the business that have been optimized by process. They follow the guidelines and come to me with the problems they can't solve. This requires a well thought out and refined infrastructure. Having one business that is 80% self managed with the right processes and people in place, you can manage another that requires more attention. Build that business to a point of self managed and rinse and repeat.
Rome was not built in a day and Caesar certainly didn't try to build two of them at once.