If I run 3 different businesses out of 1 home office, do I divide the square footage of the home office by 3, so that each business is allowed 1/3 of that footage?

Here are the methods the IRS allows you to use for this situation.

Under the actual expense method, you would need to figure out the percentage of time that the office space was used for each business. Then the usage percentage of each is applied to every home office expense in each separate business. This method would require that you keep accurate records of the time you worked in the home office throughout the year. If you didn’t keep accurate records of the time you worked in the home office, you could consider another reasonable method instead. you must use the same method from year to year,

Yes, you can use the same home office space for more than one business that's reported on Schedule C.  You can divide it based on the time you spend using it for each business, the square feet you use for each business, or  based on a combination.

Refer to the TurboTax article Can I claim the home office deduction for two or more businesses? for more information.