Single SSH login for multilpe machines?

I have a number of physical (desktop) machines running at the office as part of a new network to handle processing & serving Open Source data; some of these machines also house VMs.

At the moment, if an employee wants admin access to this network, I have to manually create accounts on each machine and set up the SSH key for each one (~12 in all).

Is it possible to introduce a new machine that can act as an SSH login node, that once logged into will allow access to all the other machines? Could it also allow new accounts to be created and configured on the login node, then propagate that to the "compute" nodes?

I can handle administrating a single Unix node, but networking them is new to me. What technologies would I need to handle this (if it's possible)?

Thanks in advance!

Adding those users to each machine will turn into a PITA! Most people would hook them into the AD forest or perhaps implement some other proper LDAP solution. You could always go backwards and implement NIS I suppose? Worst case, just SCP the /etc/passwd, /etc/shadow and /etc/groups to each node after you've added the users to one. Nowdays Ansible is the cool thing and it would likely help you do a number of other things that will ultimately have to be done on each machine in your fleet at some point or another.

Adding local accounts on each machine works, but this may turn into an issue down the road. Why we have NIS, LDAP & AD. One place to go to deactivate a user and its reflected across your entire fleet. If you get any of the standard industry security audits, you will likely fail unless you implement a common access and authorization solution like LDAP or AD.