We describe the design and implementation of a fourth version of the TripleSpec near-infrared spectrograph (TSpec4). This version of the instrument was designed for and first implemented on the 4-m Blanco telescope on Cerro Tololo, and subsequently converted for use on the 4-m Southern Astrophysical Research (SOAR) Telescope on Cerro Pachon. Details of the changed opto-mechanical design and mounting arrangements are discussed. An updated data pipeline provides reduced spectra from the instrument. We describe the required modifications and the performance of both implementations of TSpec4. The move from the Blanco to SOAR required changing from operation at a classical Cassegrain f/8 focus to operation at a Nasmyth f/16 focus. The SOAR mount also employs a rotator and required accommodation to a significantly different back-focal distance inside the instrument. These changes were implemented by modifying the instrument fore-optics which feeds light onto the slit at f/10.6. The spectrograph and slit viewer optics are unchanged. A dichroic reflects infrared light toward the instrument while passing visible light to a SOAR facility guider; this removes the shortest wavelengths from the spectra and in turn required modification of the data reduction pipeline. As the telescopes have similar apertures, the performance of the instrument is similar on both, though on SOAR image quality is somewhat better and details of the instrument's optical properties differ also. Flexure performance differs as well due to the different instrument locations.