Patients with multifocal, multicentric and synchronous bilateral breast cancers are allowed* Multifocal disease is defined as more than one invasive cancer < 2 cm from the largest lesion within the same breast quadrant; (NOTE: the Oncotype DX testing must be completed on the largest lesion)* Multicentric disease is defined as more than one invasive cancer >= 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants (NOTE: Oncotype DX testing should be completed on all tumors and the determination for eligibility should be made on the highest recurrence score)* Synchronous bilateral disease is defined as invasive breast cancer with positive lymph nodes (axillary or intramammary) in at least one breast, diagnosed within 30 days of each other; (NOTE: the Oncotype DX testing should be completed on both tumors and the tumor with the highest recurrence score should be used)
Patients must not have inflammatory breast cancer and must not have metastatic disease
Patients must not have begun chemotherapy or endocrine therapy for their breast cancer prior to registration
Step 2 Registration must take place within 84 days after definitive surgery; patients must not have begun chemotherapy or endocrine therapy for their breast cancer prior to randomization
Life expectancy of at least 5 years, excluding diagnosis of breast cancer (comorbid conditions should be taken into consideration, but breast cancer diagnosis is not a consideration)
Bilateral mammogram =< 90 days prior to date of surgery; Note: for patients undergoing more than 1 breast operation, this is the date of the first breast surgery for breast cancer treatment
Planned partial breast radiation
Patients with known breast cancer (BRCA) mutations; patients who are not tested or whose testing result is not returned at the time of registration are not excluded from registering to this study
Women who have undergone a total mastectomy or breast-conserving surgery for primary breast cancer +/- chemotherapy, +/- radiotherapy
Patients must not have metastatic breast cancer (stage IV disease); patients with multifocal, multicentric, and synchronous bilateral, and primary inflammatory breast cancers are allowed* Multifocal disease is defined as more than one invasive cancer < 2 cm from the largest lesion within the same breast quadrant* Multicentric disease is defined as more than one invasive cancer >= 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants* Synchronous bilateral disease is defined as invasive breast cancer with positive lymph nodes (axillary or intramammary) in at least one breast, diagnosed within 30 days of each other; (NOTE: the tumor with the highest recurrence score should be used)
Pathologically confirmed diagnosis of breast cancer, clinical stage I-II (T1-3 N0 M0, T0-2 N1 M0); diagnosis must be by needle biopsy; patients diagnosed by surgical excision are excluded; for patients enrolled after receipt and completion of neoadjuvant chemotherapy, the clinical stage must be determined based on pre-chemotherapy assessment
No patients with bilateral breast cancer
No patients with known deleterious mutations in breast cancer (BRCA) genes
No patients scheduled to receive partial breast irradiation following breast conserving surgery
Providing surgical treatment for newly diagnosed breast cancer patients
Newly diagnosed primary breast cancer prior to initial definitive surgical treatment, including in situ and invasive cancer, stages 0  III; pathologic confirmation of diagnosis is required
T4 tumors including inflammatory breast cancer
Any radiation therapy for the currently diagnosed breast cancer prior to randomization
Clinical stage T1-3 N1 M0 breast cancer at diagnosis (prior to the start of neoadjuvant chemotherapy) by American Joint Committee on Cancer (AJCC) staging 7th edition
No inflammatory breast cancer
Pathologic confirmation of invasive breast cancer diagnosed by core needle biopsy
Clinical T2-T4c, any N, M0 invasive breast cancer, by American Joint Committee on Cancer (AJCC) 7th edition clinical staging, with the goal being surgery to complete excision of the tumor in the breast and the lymph nodePrimary tumor must be:* Palpable* Its largest tumor diameter is > 2.0 cm by physical examination or by radiological assessment* Bi-dimensional measurement by tape, ruler or caliper technique must be provided** Note:*** Patients with contralateral ductal carcinoma in situ and/or invasive breast cancer are not eligible*** Patients with multi-focal breast cancer (defined as more than one lesion of invasive breast cancer in the same breast separated from the dominant breast lesion by less than 5 cm of radiologically normal breast tissue) are eligible; if the other lesions have been biopsied (biopsy not required) they must meet the estrogen receptor/human epidermal growth factor receptor 2 (ER/HER2) eligibility requirements; research biopsies and Ki67 assessment and radiological measures are to be performed on the dominant breast lesion
Inflammatory breast cancer defined as clinically significant erythema of the breast and/or documented dermal lymphatic invasion (not direct skin invasion by tumor or peau dorange without erythema)
An excisional biopsy of this breast cancer
Breast implants are contraindicated only if the implant precludes the required research biopsies or interferes with palpating the breast lesion
Patients with breast cancer must have had at least one prior chemotherapy regimen for metastatic disease; additionally, patients with breast cancer must have received prior tamoxifen and/or aromatase inhibitor therapy (if post-menopausal) with at least one hormonal regimen in the metastatic setting; patients with HER2+ breast cancer must have progressed after at least one prior HER2-directed regimen (trastuzumab, lapatinib) for metastatic disease* All other patients must have disease that has progressed following at least one line of standard therapy; prior therapy with tamoxifen is allowed
Stage I-III breast cancer (including inflammatory and newly diagnosed recurrent breast cancer) or lymphoma stage I-IV; (patients should have a > 2 year life expectancy)
Completed adequate breast surgery defined as:* The inked margins of breast conservation surgery or mastectomy must be histologically free of invasive breast cancer and ductal carcinoma in situ with the exception of the posterior margin if this margin is the pectoralis major fascia or the anterior margin if this is the dermis; patients with resection margins positive for lobular carcinoma in situ are eligible* Patients with breast conservation must have adjuvant radiotherapy; patients having mastectomy may have adjuvant radiotherapy according to local policy and/or international guidelines
Pathologically confirmed metastatic breast cancer
The interval between the last surgery for breast cancer (including re-excision of margins) and randomization must be no more than 60 days
T4 tumors including inflammatory breast cancer
Chemotherapy administered for the currently diagnosed breast cancer prior to randomization
Histologically confirmed metastatic breast cancer
Any number of prior therapies for metastatic breast cancer is allowed; patients with weakly estrogen receptor positive breast cancer who received any number of endocrine agents for metastatic breast cancer will also be eligible
Breast cancer for which patient is receiving endocrine therapy must have been histologically-proven stage I-III, endocrine-responsive (i.e., estrogen and/or progesterone receptor positive, according to local definition of positive, determined using immunohistochemistry [IHC]), and treated with curative intent* Note:** Patients with synchronous bilateral invasive breast cancer (diagnosed histologically within 2 months) are eligible** Patient with invasive breast cancer or synchronous bilateral invasive breast cancer (diagnosed histologically within 2 months) during pregnancy are eligible** Patients with breast cancer 1/2, early onset (BRCA1/2) mutations are eligible** Patients could have received neo/adjuvant chemotherapy, or other systemic therapy (e.g., neo/adjuvant human epidermal growth factor receptor 2 [HER2]-targeted therapy) according to institutional policy and patients desire
Patient must be premenopausal at breast cancer diagnosis, as determined locally and documented in patient record; (Note: it is understood that patients menopausal status may be unclear at the time of study enrollment)
Post-menopausal patients at breast cancer (BC) diagnosis, as determined locally
Patients with current local, loco-regional relapse and/or distant metastatic breast cancer
Subjects must have histologically confirmed invasive breast cancer and registration must occur within 12 months after the first histologic diagnosis of invasive breast cancer* A core biopsy interpreted as invasive cancer meets this criterion; if no core biopsy is performed, the date of first histologic diagnosis will be the date of first surgical procedure that identifies invasive cancer (biopsy, lumpectomy or mastectomy)* Neoadjuvant subjects should have no evidence of clinical T4 disease prior to chemotherapy and surgery; eligibility for neoadjuvant patients can be defined by either clinical stage prior to therapy or pathologic stage at surgery; if patient is eligible based on either, they are eligible for the study* Bilateral breast carcinoma is allowed provided either:** Diagnoses are synchronous  that is, within 3 months of one another  and at least one of the two breast carcinomas meet the eligibility criteria and neither is Her-2 positive or inflammatory; OR** The contralateral breast cancer was at least 5 years prior to the current diagnosis* No evidence of metastatic disease
Patients breast density must be known; patients must have mammographically dense breasts, American College of Radiology (ACR) Breast Imaging (BI)- Reporting and Data System Atlas (RADS) lexicon categories c or d (heterogeneous or extreme fibroglandular tissue) on their most-recent prior screening
Patient must not be taking chemoprevention for breast cancer
Patient must not have undergone breast ultrasound within 12 months prior to randomization
Patient must not be suspected of being at high-risk for breast cancer, as defined by the American Cancer Society (ACS) breast MR screening recommendations (lifetime risk of >= 20-25%)
Patients must have histologically confirmed new diagnosis of breast cancer
For the dose expansion cohort, patients with triple-negative breast cancer may not be BRCA1/2 germline mutation carriers
Patients must be undergoing breast conserving therapy
T4 tumors including inflammatory breast cancer
Patients must not have symptoms or signs of benign or malignant breast disease (e.g., bloody or clear nipple discharge, breast lump) based on physician physical exam or self breast exam; patients with breast pain are eligible as long as other criteria are met
Patients must not currently have breast enhancements (e.g., implants or injections)
To be eligible for inclusion in the annual screening regimen one of the following three conditions must be met in addition to the eligibility criteria above:* Patients are pre-menopausal; OR* Post-menopausal aged 45-69 with any of the following three risks factors:** Dense breasts (BIRADS density categories c-heterogeneously dense or d-extremely dense), or** Family history of breast cancer (first degree relative with breast cancer), or, participant positive genetic testing for any deleterious genes that indicate an increased risk for breast cancer, or** Currently on hormone therapy; OR* Post-menopausal ages 70-74 with either of the following two risk factors:** Dense breasts (BIRADS density categories c-heterogeneously dense or d-extremely dense), or** Currently on hormone therapy