Yes, you can, depending on the brand, your experience and how much you are willing to invest. There are two ways to own more than one franchise. 'Multi-unit' and 'multi-brand'.
1. Multi-Unit Ownership:
You obtain the rights to operate several locations of the same brand in a region. This often comes with discounts and exclusive territory rights.
Brands prefer experienced franchisees, so if you have been franchisee before, that will give you a better chance of becoming a multi-unit franchisee. If you haven't previously been a franchisee, they would generally expect some level of management experience for multi-unit.
Some brands offer multi-unit opportunities from the start, with the right managers and available capital. Others prefer that you open a single franchise location first. Once you have proven your ability to succeed in the brand, you may then expand to multiple units.
2. Multi-Brand Ownership:
You invest in different, non-competing franchises - like owning a coffee shop and a gym franchise.
This diversifies your income and spreads the risk for you, however some brands may not be OK with this as you are no longer focused on just their brand. These opportunities must be explored with the individual franchisors.