A leasehold agreement where the base rent changes is called a:

A lease-purchase agreement combines leasing with an option to buy the property at the end of the lease term. While it may involve different payment structures, the base rent in a lease-purchase agreement typically remains fixed throughout the lease duration, thus not qualifying as a variable lease.

A percentage lease involves rent payments that are based on a percentage of the tenant's sales revenue, often used in retail settings. Although the rent can change based on sales performance, it does not represent a base rent that adjusts independently of sales, which defines a variable lease.

A net lease requires the tenant to pay additional costs such as property taxes, insurance, and maintenance on top of the base rent. While this type of lease can impact total costs, the base rent itself remains fixed, distinguishing it from a variable lease where the base rent itself changes.