The CALorimetric Electron Telescope (CALET) on the International Space Station (ISS) has made cosmic-ray observations since shortly after its launch in August 2015. The heart of CALET, its main calorimeter (CAL), continues to make the direct measurements of the highest energy cosmic ray total electron spectrum it was designed for. The CAL has also observed gamma rays and cosmic-ray (CR) nuclei, and it has measured energy spectra as well as secondary to primary ratios of the more abundant CR nuclei through $_{26}$Fe. In addition, the CAL has measured the ultra-heavy cosmic ray (UHCR) nuclei heavier than $_{26}$Fe, and it has demonstrated the dynamic range to measure CR nuclei from $_{1}$H to $_{40}$Zr. Using the main high energy (HE) CAL trigger mode particle energies can be reconstructed from the energy deposition in the total absorption calorimeter (TASC), and there is also a high duty cycle (∼90%) UHCR trigger providing an expanded geometric acceptance that is ∼6× that for events fully contained by the CAL. In ∼5 years the UHCR trigger will collect a data set comparable to that so far collected by the balloon-borne SuperTIGER instrument. Preliminary CALET results presented at the last ICRC were in reasonable agreement with SuperTIGER relative abundances of even charge UHCR nuclei in a similar energy range. Both of these measurements are complemented by the ∼1/3 smaller lower-energy space-based ACE-CRIS measurements. We present the current status and future plans for the CALET UHCR analysis.