What do you do for patients with HR+ inflammatory breast cancer who do not achieve a pCR with neoadjuvant chemotherapy?

I assume the patient in this question is HER2 negative. Inflammatory breast cancer is rarely HR+, HER2-, but for HR+ HER2- invasive breast cancer who do not achieve pCR with neoadjuvant chemotherapy, I would recommend to maximize the benefit of adjuvant hormone therapy.

The patient certainly could join a clinical trial such as PALLAS trial or S1207 trial. If a clinical trial is not available or not an option, for premenopausal patients, the addition of ovarian suppression to standard antiestrogen...

I concur - my only suggestion would be the addition of a bone-protecting agent such as zoledronic acid to her adjuvant regimen, since bone is a common site of first recurrence in the ER+/HER2- subtype, even though inflammatory cancers are more likely to recur at visceral sites than non-inflammatory cancers.