Is there any way we can increase the number of RDP sessions available to our Dedicated Server (unmanaged)?

RDP/Terminal Services runs in 2 modes, administrative or application.  Windows Server licensing includes support for administrative mode, which includes 2 sessions.  To run Terminal Services in application mode, which can support more than 2 terminal services sessions, additional licensing is required.  If you would like pricing information on this, submit a request to the billing team, and identify the max number of concurrent sessions you would like available.