I believe that under federal law, the franchise owner cannot avoid overtime in this way.
A similar case was considered by the Labor Department in 2005 (FLSA2005-17NA):
This is in response to your request for an opinion concerning the application of the overtime requirements of section 7 of the Fair Labor Standards Act (FLSA) to employees who work at two different health care facilities operated by one management company. It is our opinion that all hours worked at any of the facilities must be combined for the purpose of calculating hours worked under the FLSA.
The letter explains the logic pretty clearly, with citations. When an employee is "jointly" employed by two or more employers, then the hours are all combined for overtime purposes. 29 CFR 791.2(b) explains how "jointly" is determined:
Where the employee performs work which simultaneously benefits two or
more employers, or works for two or more employers at different times
during the workweek, a joint employment relationship generally will be
considered to exist in situations such as:
(1) Where there is an arrangement between the employers to share the
employee's services, as, for example, to interchange employees; or
(2) Where one employer is acting directly or indirectly in the
interest of the other employer (or employers) in relation to the
(3) Where the employers are not completely disassociated with respect
to the employment of a particular employee and may be deemed to share
control of the employee, directly or indirectly, by reason of the fact
that one employer controls, is controlled by, or is under common
control with the other employer.
Paragraph (1) applies: the two employers (the two restaurants) have an arrangement to share the employee's services (the owner is explicitly dividing their hours). Paragraph (3) also applies: both employers are under common control, since the same person owns both. They certainly are "not completely dissociated".
The same logic would seem to apply even if the two locations are different restaurants, or different types of businesses.
The 2005 letter explains further:
Factors that are relevant in finding joint employment include, for example, whether there are common officers or directors of the companies; the nature of the common management support provided; whether employees have priority for vacancies at the other companies; whether there are any common insurance, pension or payroll systems; and whether there are any common hiring seniority, recordkeeping or billing systems.
These also seem likely to apply in your hypothetical cases.