How do you manage anaplastic thyroid cancer that is progressing through radiation therapy?  

The algorithms for ATC, a rare disease, have gotten relatively complex including the incorporation and timing of XRT. It is unclear from the question what the presentation scenario is, i.e., localized disease or metastatic, and the mutational status, as ideally at a minimum BRAF status is known. Now...

Would get NGS asap. If BRAF V600E mutation or NTRK, RET fusions noted, start targeted treatment immediately. Otherwise, look for clinical trials. Chemo has minimal benefit. There is emerging data for combining checkpoint inhibitors with lenvatinib (for those without targetable mutations).