What kind of phone system can control client calling access with individual PINs?

The answer depends heavily on how the four phones are currently set up. If each phone is an extension behind a PBX, this may be fairly straightforward. If the phones are directly tied to individual numbers or extensions, you may only be able to assign one PIN per extension. Users would likely need to authenticate on the phones or use a system designed specifically for per-user calling access.

Before choosing a platform, get the requesting manager to define the scope, budget, staffing, and ongoing operations responsibilities. A system like this needs more than phones: you may need a PBX or hosted service, user authentication, custom scheduling logic, network configuration, and support procedures for adding and removing clients. If the requirement is genuinely necessary, a specialized provider may cost more up front but avoid turning your team into the system administrator.

Asterisk could technically handle all of these requirements, but it would probably become a custom application rather than a simple configuration. You would need to build the PIN workflow, calling schedules, time limits, lockouts, staff overrides, and client admission/discharge process. Make sure the organization is prepared to fund both the initial development and ongoing maintenance.

Most PBX platforms can provide pieces of this, such as PIN-based dialing, call restrictions, schedules, and administrative overrides. The difficult requirement is tying a PIN to a specific authorized calling period and automatically preventing reuse afterward. That feature is more common in specialized correctional or healthcare systems than in ordinary business VoIP products, so comparing vendors that already serve those environments may be more practical than building it internally.