This study will evaluate the safety, tolerability, and preliminary effectiveness of AMXT 1501 and DFMO when combined with standard treatments for advanced solid tumors. The trial includes two groups:

* Cohort 1: Patients with ER+ / HER2- breast cancer receiving fulvestrant and capivasertib
* Cohort 2: Patients with unresectable or metastatic cutaneous melanoma receiving pembrolizumab

The Phase 1b portion will find the recommended Phase 2 dose (RP2D). The Phase 2 portion will further evaluate clinical activity at the RP2D using response criteria for solid tumors (RECIST 1.1).

The study will also evaluate pharmacokinetics, pharmacodynamics, disease control, and overall safety.