The confusion in this conversation is the language that the CSR vs us use.
The CSR said you can have more than one Genie, which we know is not true ...
However, the CSR is calling the Genie CLIENT-Mini a Genie, which is where the confusion comes in.
In Order to have 4k, you need (as Jason mentioned) the C61k mini-genie client.
The clients work off the Main Genie .... (more confusion).
The main Genie is one of two different types .... The Genie (Original) is a HR34 (not used anymore for new subs), HR44 and HR54, While the HR44 is a very good unit, it doesn't handle the 4K your inquiring about, so you would want a HR54 and a 4k capable client and any variety of other client (for the 3rd TV) .
The other Genie (Genie 2) they use (not for new subs in most cases) is the HS17 (home server, which doesn't allow any of the other type of recvrs out there (HR24's which is the stand alone unit that I would suggest and Jason mentioned).
If you can, I would go with a HR54 a C61k mini-genie client and a HR24, this would give you 7 tuners available to you.
Also, so you know, the 4k client (or any client) doesn't have a tuner at all, so it uses its tuners and recording capability from the Genie you decide on.