The following quote came from Registration and Title Bulletin - #019-11
which references the software application, "Registration and Title System (RTS) Version 6.7.0", that County Tax Assessor-Collectors use when registering vehicles in the State of Texas. The IVTRS is used by those that are registering a vehicle online... so it looks like you can register for 12, 24, or 36 months.
With this release, Multi-Year Registration will be available for most new and used vehicle types and customers will have the option of paying registration fees for 12, 24 or 36 months at time of title transfer or registration renewal. Customers will also have the option to renew online, through IVTRS, for 12, 24 or 36 months in participating counties."