I would recommend creating a Custom User Role, using the
add_role() function, such as a "Site Admin" or "Sub-Admin" (or whatever you want to call it). Then, you can assign specific user capabilities to that custom role, thereby giving users exactly the capabilities you want them to have, without giving them the capabilities you don't want them to have.
// Role slug
// Role display name
(Those are the default "administrator" capabilities, with caps related to editing others' pages, and promoting users, removed.)
There are several Plugins available that provide a UI for creating and modifying user roles, including: