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.

Difluoromethylornithine (DFMO) will be used in an open label, single agent, multicenter, study for patients with neuroblastoma in remission. In this study subjects will receive 730 Days of oral difluoromethylornithine (DFMO) at a dose of 750 mg/m2 250 mg/m2 BID (strata 1, 2, 3, and 4) OR 2500 mg/m2 BID (stratum 1B) on each day of study. This study will focus on the use of DFMO in high risk neuroblastoma patients that are in remission as a strategy to prevent recurrence.