The goal of this clinical trial is to evaluate the safety of TOS-358 in adults with select solid tumors who meet study enrollment criteria. The main questions it aims to answer are:

1. what is the maximum tolerated dose and recommended dose for phase 2?
2. how safe and tolerable is TOS-358 at different dose levels when taken orally once or twice per day?

This research study is studying a combination of HER2-directed therapies (trastuzumab and pertuzumab) and hormonal therapy as a treatment after surgery for hormone receptor positive breast cancer.

The study drugs involved in this study are:

* A combination of trastuzumab and pertuzumab given as an injection under the skin (PHESGO)
* Hormonal (endocrine) Treatment

This phase II trial tests how well evaluating circulating tumor deoxyribonucleic acid (ctDNA) works to guide therapy-change decisions in treating patients with triple-negative breast cancer (TNBC) that has spread from where it first started (primary site) to other places in the body (metastatic). This study wants to learn if small pieces of DNA associated with a tumor (called circulating tumor DNA, or ctDNA) can be detected in investigational blood tests during the course of standard chemotherapy treatment for breast cancer, and whether information from such investigational ctDNA blood testing could possibly be used as an early indication of chemotherapy treatment failure. It is hoped that additional information from investigational blood testing for ctDNA could help doctors to switch more quickly from a standard chemotherapy treatment that typically has significant side effects and which may not be working, to a different standard treatment regimen against TNBC, called sacituzumab govitecan. Sacituzumab govitecan is a monoclonal antibody, called hRS7, linked to a chemotherapy drug, called irinotecan. hRS7 is a form of targeted therapy because it attaches to specific molecules (receptors) on the surface of cancer cells, known as TROP2 receptors, and delivers irinotecan to kill them. Studying ctDNA may assist doctors to change therapy earlier if needed, and may improve health outcomes in patients with metastatic TNBC.

This is an umbrella study evaluating the efficacy and safety of multiple treatment combinations in participants with metastatic or inoperable locally advanced breast cancer.

The study will be performed in two stages. During Stage 1, six cohorts will be enrolled in parallel in this study:

Cohort 1 will consist of programmed death-ligand 1 (PD-L1)-positive participants who have received no prior systemic therapy for metastatic or inoperable locally advanced triple-negative breast cancer (TNBC) (first-line \[1L\] PD-L1+ cohort).

Cohort 2 will consist of participants who had disease progression during or following 1L treatment with chemotherapy for metastatic or inoperable locally-advanced TNBC and have not received cancer immunotherapy (CIT) (second-line \[2L\] CIT-nave cohort).

Cohort 3, 5, and 6 will consist of participants with locally advanced or metastatic hormone receptor-positive (HR+), human epidermal growth factor receptor 2 (HER2)-negative disease with one or more PIK3CA mutations.

Cohort 4 will consist of participants with locally advanced or metastatic HER2+ /HER2-low disease with one or more PIK3CA mutations who had disease progression on standard-of-care therapies (HER2+ /HER2-low cohort).

In each cohort, eligible participants will initially be assigned to one of several treatment arms (Stage 1). During Stage 2, participants in the 2L CIT-nave cohort who experience disease progression, loss of clinical benefit, or unacceptable toxicity during Stage 1 may be eligible to continue treatment with a different treatment combination, provided Stage 2 is open for enrollment and all eligibility criteria are met.

This phase Ib trial tests the safety and tolerability of ZEN003694 in combination with an immunotherapy drug called pembrolizumab and the usual chemotherapy approach with nab-paclitaxel for the treatment of patients with triple negative-negative breast cancer that has spread to other parts of the body (advanced). Paclitaxel is in a class of medications called antimicrotubule agents. It stops cancer cells from growing and dividing and may kill them. Nab-paclitaxel is an albumin-stabilized nanoparticle formulation of paclitaxel which may have fewer side effects and work better than other forms of paclitaxel. Immunotherapy with monoclonal antibodies, such as pembrolizumab may help the body's immune system attach the cancer and may interfere with the ability of tumor cells to grow and spread. ZEN003694 is an inhibitor of a family of proteins called the bromodomain and extra-terminal (BET). It may prevent the growth of tumor cells that over produce BET protein. Combination therapy with ZEN003694 pembrolizumab immunotherapy and nab-paclitaxel chemotherapy may help shrink or stabilize cancer for longer than chemotherapy alone.

This research is to evaluate the effectiveness of Talazoparib as a potential treatment for metastatic breast cancer with a BRCA 1 or BRCA 2 mutation.

Persons with secondary arm and/or upper quadrant lymphedema following cancer therapies commonly are prescribed complete decongestive therapy as a course of management of their lymphedema. The investigators will perform a repeated-measures cross-over trial to test the hypothesis that mobilization of protein enriched hardened tissue using graded negative pressure therapy in conjunction with complete decongestive therapy (CDT) is more effective to standard CDT alone for secondary lymphedema management.

This phase II trial studies how well the combination of avelumab with liposomal doxorubicin with or without binimetinib, or the combination of avelumab with sacituzumab govitecan works in treating patients with triple negative breast cancer that is stage IV or is not able to be removed by surgery (unresectable) and has come back (recurrent). Immunotherapy with checkpoint inhibitors like avelumab require activation of the patient's immune system.

This trial includes a two week induction or lead-in of medications that can stimulate the immune system. It is our hope that this induction will improve the response to immunotherapy with avelumab. One treatment, sacituzumab Govitecan, is a monoclonal antibody called sacituzumab linked to a chemotherapy drug called SN-38. Sacituzumab govitecan is a form of targeted therapy because it attaches to specific molecules (receptors) on the surface of tumor cells, known as Tumor-associated calcium signal transducer 2 (TROP2) receptors, and delivers SN-38 to kill them. Another treatment, liposomal doxorubicin, is a form of the anticancer drug doxorubicin that is contained in very tiny, fat-like particles. It may have fewer side effects and work better than doxorubicin, and may enhance factors associated with immune response. The third medication is called binimetinib, which may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth, and may help activate the immune system. It is not yet known whether giving avelumab in combination with liposomal doxorubicin with or without binimetinib, or the combination of avelumab with sacituzumab govitecan will work better in treating patients with triple negative breast cancer.

The phase III trial compares the effect of pembrolizumab to observation for the treatment of patients with early-stage triple-negative breast cancer who achieved a pathologic complete response after preoperative chemotherapy in combination with pembrolizumab. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. This trial may help researchers determine if observation will result in the same risk of cancer coming back as pembrolizumab after surgery in triple-negative breast cancer patients who achieve pathologic complete response after preoperative chemotherapy with pembrolizumab.