The system is set up to only recognize one registered website admin per club. This is by design.
However, as you note, you can certainly share your admin password.
Additionally, if you are using the Access settings, then you can delegate access to specific Admin console modules to a club officer without having to give out your admin password. Many clubs opt to do this in order to "lighten the load" on the website admin and get their club officers more involved in doing website updates. For example, in my club, we expect the VPM to update the Membership Management module with new members and guests. We train them to do that, and we use the Access Settings to delegate access to that module to the VPM. In my club, the website admin role is more of an website oversight and training role.
For more information on the Access settings, see the following:
support.toastmastersclubs.org/doc/item/access-settings