The main objective of the study is to assess whether the combination of ipatasertib and HP (+/- ET) is tolerable, especially in terms of the incidence and severity of diarrhea. For this purpose, up to a total of 25 patients will be enrolled in a staggered manner and evaluated.

A 3-cohort, descending doses (400, 300, 200 mg) design will serve to establish the Maximun Toleraded Dose (MTD) and Recommended Phase 2 Dose (RP2D) of ipatasertib in combination with HP.

The study will initially include 6 patients that will receive ipatasertib plus HP at Dose Level 1.

If 1 DLTs are observed, this dose will be deemed safe, and the trial will enroll at least additional 19 patients to further assess safety and preliminary efficacy of the combination.

If 2 DLT occurs in the first 6 patients, a decision will be made of whether expand Dose Level 1 to 10 additional patients or to de-escalate ipatasertib to the next lower dose level. In the case of de-escalation, the same rules will apply for enrollment and expansion of Dose level -1. The minimum ipatasertib dose explored will be Dose level -2.

Dose reductions of pertuzumab and trastuzumab will not be allowed.

If all inclusion criteria and no exclusion criteria are met, patients will be enrolled in the trial and will start treatment with oral (PO) ipatasertib once a day (QD) D1-21 in 28-days cycles, together with pertuzumab 420 mg intravenous (IV) every 21 days (Q21d) and trastuzumab 600 mg subcutaneous (SC) Q21d.

Patients with hormone receptor positive (HR+) tumors (defined as ER and/or PgR expression in >1% of tumor cells) will also receive endocrine therapy either an Aromatase Inhibitor (AI), tamoxifen or fulvestrant +/- Luteinizing Hormone-Releasing Hormone (LHRH) analogues, according to Investigator's decision.

Patients will also start loperamide (2 mg twice a day [BID] or 4 mg QD) as prophylaxis for diarrhea in the first cycle