How to allow more than two Remote Windows sessions on Windows Server 2012 Standard?

Recently setup a new 2012 server. After I create two Remote Windows connections to the server using ordinary user accounts (not administrators), I get this error when I try to create a third connection:

Select a user to disconnect so you can sign in
There are too many users signed in

I read that you can only have two admin connections (one physical and one virtual) but these are not admin users. In the datasheet for this product it says I can have unlimited RDS users. Wish the messages had a bit more information on this server!

Windows by default allows two RDS RDP* connections out of the box, and they are known as "administrative connections" regardless of if the user account is an administrator or not. If you need more remote connections you need to research RDS which requires it's own set of user connection licenses in addition to CALs.

RDS can allow for a number of simultaneous connections that is only limited by your bandwidth and server hardware. To do so, you will need a multi-server infrastructure of at least two machines to host the various RDS roles as well as at least one domain controller. TS Gateway and RDS Session Hosts shouldn't be included on a domain controller, but you can potentially get some of the services to work on a domain controller. It's a terrible hack that will probably break every time Windows applies patches, or it might be the opposite scenario where the hack will break certain Windows patches.

*(I edited this to clear up some of the confusion. The term "RDS" refers to a larger suite of products that implements virtual desktops and RemoteApp. RDP is the protocol and the term "Remote Desktop Connection" [RDC] is typically used to describe the generic Remote Desktop Connections that administrators would typically use to work on a server directly.)