Bilateral synchronous tumors with inheritable forms of RCC including von Hippel-Lindau Synchronous bilateral breast cancer at the time of diagnosis Unilateral, bilateral, unifocal, or multifocal DCIS Bilateral DCIS: bilateral breast imaging ? 90 days of registration (must include bilateral mammogram; can also include ultrasound or breast MRI) Patients must have had a bilateral mammogram within 12 months prior to registration, unless the initial surgery was a total mastectomy, in which case only a mammogram of the remaining breast is required; (subjects with bilateral total mastectomies do not require imaging) Patients with synchronous bilateral invasive disease are eligible as long as all the lesions assessed for HER2 on both sides are negative Patients with current and symptomatic pneumonitis, or extensive bilateral lung disease on high resolution CT scan Participants with bilateral diffuse lymphangitic carcinomatosis Women who have had a prior mastectomy (unilateral or bilateral), segmental mastectomy, reduction mammoplasty or breast augmentation including implants. Bilateral breast cancer Bilateral breast cancer is permitted; patients with bilateral breast cancer will be stratified as left-sided Prior bilateral orchiectomy Male is sterile due to a bilateral orchiectomy Multifocal gliomas that are bilateral; patients with unilateral multifocal gliomas may be eligible if their multifocal disease can be treated effectively and safely in a single MLA procedure; also note that corpus callosal tumors are eligible even if they are bilateral as long as they satisfy the size and shape limits of MLA as determined by the performing neurosurgeon Patients with simultaneous primaries or bilateral tumors are excluded, with the exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0 resected differentiated thyroid carcinoma, who are eligible Synchronous bilateral breast cancer at the time of diagnosis Extensive bilateral lung disease on high-resolution computed tomography (HRCT) scan Bilateral breast cancers are allowed if the treating clinician has determined the patient should be treated as ER+ and HER2- negative Bilateral invasive BC. Bilateral breast cancer Patients with simultaneous primaries or bilateral tumors are excluded, with the exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0 differentiated thyroid carcinoma (resected or management deferred), who are eligible Bilateral synchronous breast cancer Bilateral ocular adnexal involvement is permitted, if biopsy confirms unilateral disease and there is high clinical suspicion for bilateral disease, biopsy of the contralateral ocular adnexa can be waived Histologically proven unilateral or bilateral primary breast carcinoma; (in case of bilateral cancer, the investigator has to decide prospectively which side will be evaluated for the primary endpoint) Multiple or bilateral renal masses Choose bilateral mastectomy followed by bilateral immediate tissue expander breast reconstruction Multicentric or bilateral disease unless biopsy of the clinical abnormalities are performed and result is negative. Patients with bilateral synchronous renal masses Patient must have had a bilateral mammogram prior to NAC unless there is only one breast Ongoing therapy with LHRH analog or bilateral orchiectomy. Cases involving a bilateral operation Bilateral breast malignancy Patients with simultaneous primaries or bilateral tumors are excluded, with the exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0 differentiated thyroid carcinoma, who are eligible Patients with simultaneous primaries or bilateral tumors are excluded, with the exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0 resected differentiated thyroid carcinoma, who are eligible Peripheral bilateral edema requiring active medical management Patients with simultaneous primaries or bilateral tumors are excluded, with the exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0 resected differentiated thyroid carcinoma, who are eligible Bilateral prophylactic mastectomy Current unilateral or bilateral hydronephrosis Completely resected unilateral or bilateral primary carcinoma of the breast Patients with simultaneous primaries or bilateral tumors. Participants with multicentric (multiple tumors involving more than 1 quadrant) or bilateral breast cancer Physician recommendation of bilateral neck radiation History of or plans for bilateral mastectomies within the next 12 months Unilateral or bilateral retinoblastoma (RB) patients are eligible Participants with synchronous bilateral invasive disease are eligible only if both lesions are HER2-positive For subjects with two breasts, they must have had a bilateral mammogram prior to surgery Patients with synchronous bilateral breast cancers are eligible if at least one of the tumors is HER2-positive Bilateral breast cancers that individually meet eligibility criteria are allowed Prior bilateral orchiectomy Unifocal breast cancer (no evidence of gross multifocal disease, multicentric, or bilateral disease) Bilateral pulmonary metastasis Male subject is sterile due to a bilateral orchiectomy. Patients who have not had a bilateral orchiectomy must have a plan to maintain effective GnRG-analogue therapy for the duration of the trial Vasectomy or other procedure resulting in infertility (eg, bilateral orchiectomy) for >6 months Vasectomy or other procedure resulting in infertility (e.g., bilateral orchiectomy), performed at least 6 months before screening Patients with bilateral disease Prior bilateral orchiectomy Patients are having bilateral mastectomy Participants with bilateral synchronous or metachronous disease (DCIS, LCIS, ADH, ALH) are eligible Bilateral disease (diagnosed cancer in both breasts) Bilateral upper extremity LE Multiple or bilateral renal masses when more than one mass is operated on at the same time or within 4-months of each other Bilateral breast cancer Have any blood relatives diagnosed with bilateral breast cancer Bilateral tibial dysplasia Patients with bilateral upper extremity edema Patient with bilateral manipulation of axilla within the last 24 months Subjects with bilateral breast cancer are not eligible Bilateral breast cancer or planned bilateral mastectomy Subjects who have had radiation to both breasts or who have undergone bilateral mastectomies Bilateral diffuse lymphangitic carcinomatosis Prior bilateral salpingectomy; prior unilateral salpingectomy is allowed Bilateral mastectomy No patients with bilateral breast cancer Patients must have prior bilateral orchiectomy or be on continuous LHRH analogue therapy for the duration of study Bilateral hip replacement Bilateral mammography and hand-held ultrasound (if clinically indicated) performed prior to the MRI and ABUS Have bilateral breast cancer History of bilateral orchidectomy Presence of bilateral hip replacement prostheses Patients with synchronous bilateral breast cancers Ipsilateral diagnostic mammogram within 12 months of enrollment Ipsilateral breast had a previous cancer and/or prior in-field radiation Unilateral DCIS: contralateral normal mammogram ? 6 months of registration and ipsilateral breast imaging ? 90 days of registration (must include ipsilateral mammogram; can also include ultrasound or breast MRI) Any previous history of ipsilateral invasive breast cancer or ipsilateral DCIS; (patients with synchronous or previous ipsilateral LCIS are eligible) Any prior history, not including the index cancer, of ipsilateral invasive breast cancer or ipsilateral DCIS treated with radiation therapy; (patients with synchronous or previous ipsilateral LCIS are eligible) Any history, not including the index cancer, of ipsilateral or contralateral invasive breast cancer or ipsilateral or contralateral DCIS treated with radiation therapy (RT)\r\n* Note: Patients with synchronous or previous ipsilateral LCIS are eligible Recurrent ipsilateral breast cancer Open surgery in ipsilateral breast within 1 year. Radiation therapy to ipsilateral breast [Period 1] Previous history of ipsilateral invasive breast cancer or ipsilateral DCIS. (Patients with synchronous or previous ipsilateral LCIS are eligible.) Prior radiotherapy to the ipsilateral chest wall or ipsilateral breast or thorax; individuals with prior radiotherapy in the contralateral breast or chest wall are eligible No prior radiation to the ipsilateral breast History of ipsilateral breast cancer treated with radiation therapy Redo ipsilateral thoracotomy No prior radiation to the ipsilateral breast, a history of contralateral breast radiation is permitted History of ipsilateral cosmetic or reconstructive breast surgery Prior history of breast cancer or in-field radiation in the ipsilateral breast Prior radiotherapy to the ipsilateral chest wall or breast for any malignancy Prior or concurrent ipsilateral radiation therapy for invasive or noninvasive BC. Patients for whom radiotherapy for breast cancer is contraindicated because of medical reasons (e.g., connective tissue disorder or prior ipsilateral breast radiation) History of ipsilateral invasive breast cancer or ipsilateral ductal carcinoma in situ (DCIS); Note: patients with history of ipsilateral lobular carcinoma in situ (LCIS) are eligible Previous breast radiation on ipsilateral side or thoracic radiation on the ipsilateral side No prior history of lung resection on ipsilateral side Patients with a history of prior breast cancer in the ipsilateral breast treated with lumpectomy alone (no RT) are eligible as long as the other entry criteria for this study are met Prior ipsilateral breast or thoracic radiation for any condition Previous history of ipsilateral invasive breast cancer or DCIS. Any previously treated breast carcinoma or synchronous breast carcinoma in ipsilateral breast. Prior radiation therapy to the ipsilateral breast or thorax. No history of irradiation of the ipsilateral breast No evidence of other areas worrisome for cancer on physical examination and mammography of the ipsilateral breast A history of irradiation to the ipsilateral breast Clinically detected or palpable disease prior to biopsy in either breast or ipsilateral axilla Any previous history of ipsilateral invasive breast cancer or ipsilateral DCIS; (patients with synchronous or previous ipsilateral LCIS are eligible) Patients must not have received any prior treatment of any kind to treat the current breast cancer – including chemotherapy or endocrine therapy; in addition, any history of prior irradiation to the ipsilateral breast is excluded Previous radiation therapy to the ipsilateral breast Patients with a history of ipsilateral DCIS are eligible Previous radiation therapy to the ipsilateral breast Ipsilateral mammogram done greater than 6 months prior to study Patients must be a candidate for ipsilateral radiation therapy History of ipsilateral breast cancer Prior history of ipsilateral breast cancer Prior radiation therapy to the ipsilateral breast or thorax History of ipsilateral invasive breast cancer regardless of treatment or ipsilateral ductal carcinoma in situ (DCIS) treated with radiotherapy or contralateral invasive breast cancer at any time. Prior history of radiation therapy to the ipsilateral breast and/or regional nodes is not allowed (prior RT to other sites is permitted). Patients with ipsilateral treatment for DCIS or breast cancer within 12 months prior to entering this study Previous breast radiation on either side or thoracic radiation on the ipsilateral side Histological or cytological diagnosis of ES-SCLC (Note: Extensive-stage disease is defined as disease beyond the ipsilateral hemithorax, mediastinum and ipsilateral supraclavicular area and including malignant pleural or pericardial effusion or hematogenous metastases) Prior radiotherapy to the ipsilateral chest wall for any malignancy. Recurrent ipsilateral breast cancer Open surgery in the ipsilateral breast within 1 year of AVB-620 administration History of radiation therapy to ipsilateral breast Prior resection of jugular nodes ipsilateral to tumor Any prior history, not including the index cancer, of ipsilateral invasive breast cancer or ipsilateral ductal breast carcinoma in situ (DCIS) treated with radiation therapy; (Patients with synchronous or previous ipsilateral lobular breast carcinoma in situ [LCIS] are eligible) Patients that have had prior ipsilateral chestwall/thoracic radiation Previous radiation therapy to the ipsilateral breast Previous radiation to the ipsilateral breast History of prior ipsilateral lung interventions including:\r\n* Chest tube placement\r\n* Surgery\r\n* Pleurodesis\r\n* Radiation treatment Normal ipsilateral fibula without planned fibular osteotomy at time of surgery Prior radiation therapy to the ipsilateral breast/nodes or thorax Prior radiation therapy to the ipsilateral chest wall or thorax Patients with prior radiation to the breast/chest wall of the ipsilateral breast Prior receipt of ipsilateral breast or chest wall radiation Prior radiation therapy to the breast or ipsilateral regional nodes not allowed (a history of radiation therapy to other sites is permissible) Subject has a history of recurrent breast cancer in the ipsilateral breast Patients with a prior history of ipsilateral breast cancer Participants with prior history of ipsilateral breast carcinoma treated with BCS and radiation therapy Participants with prior history of ipsilateral breast carcinoma Prior history of breast cancer in the ipsilateral breast Patients must not have previous ipsilateral invasive breast cancer or DCIS Have a recurrence of ipsilateral breast cancer Prior history of ipsilateral breast cancer Prior ipsilateral breast cancer surgeries, mastectomies, breast reconstructions or implants. Prior ipsilateral reduction mammoplasties (breast reductions) performed less than 2 years prior to enrollment to this study. Prior breast malignancy of the ipsilateral breast. Patients with prior ipsilateral thoracic or breast radiation Patients with recurrent ipsilateral DCIS Synchronous or previous contralateral invasive breast cancer; (patients with synchronous and/or previous contralateral DCIS or LCIS are eligible) No history of prior or concurrent contralateral invasive breast cancer; benign breast disease; LCIS or DCIS of contralateral breast is allowed For those patients who also undergo contralateral breast surgery, if invasive disease is found in the contralateral breast, the patient is not eligible for registration /randomization History of invasive breast cancer or contralateral DCIS Synchronous or previous contralateral invasive breast cancer or DCIS; (patients with synchronous and/or previous contralateral LCIS are eligible) History of ipsilateral or contralateral breast or thoracic RT for any condition History of ipsilateral or contralateral axillary surgery for any condition Synchronous contralateral breast cancer requiring RT Patients with known bilateral invasive breast cancer; patients with contralateral in situ breast carcinoma are eligible History of previously treated ipsilateral or contralateral breast carcinoma is not an exclusion criteria if the investigator is certain newly diagnosed carcinoma is new unifocal primary tumor. Previous history of contralateral invasive breast cancer. (Patients with synchronous and/or previous contralateral DCIS or LCIS are eligible.) Invasive cancer in the contralateral breast History of prior or concurrent contralateral invasive breast cancer; benign breast disease, LCIS or DCIS of contralateral breast is allowed Invasive cancer in the contralateral breast Patients with contralateral hilar involvement Breast imaging performed prior to study registration as follows:\r\n* Ipsilateral breast – within 12 weeks\r\n* Contralateral breast – within 24 weeks Previous randomization for a contralateral procedure as part of this study Breast implant in the breast to be treated (contralateral breast implant is acceptable) Invasive cancer in the contralateral breast Invasive cancer in the contralateral breast Presence of nodules considered neoplastic in contralateral lobes (M1a) Suspicious microcalcification, densities, or palpable abnormalities (in the ipsilateral or contralateral breast) unless biopsied and found to be benign Suspicious microcalcifications, densities, or palpable abnormalities (in the ipsilateral or contralateral breast) unless these were biopsied and found to be benign Suspicious microcalcifications, or densities (in the ipsilateral or contralateral breast as documented on mammogram or breast ultrasound) unless biopsied and found to be benign Any previously treated contralateral breast carcinoma or synchronous ipsilateral breast carcinoma Patients with a prior history of contralateral breast cancer are eligible if they have no evidence of recurrence of their initial primary breast cancer Synchronous or previous contralateral invasive breast cancer; (patients with synchronous and/or previous contralateral ductal carcinoma in situ [DCIS] or lobular carcinoma in situ [LCIS] are eligible) History of any prior (ipsi- and/or contralateral) invasive breast cancer Involved contralateral hilar nodes 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 node;\r\n* The extent of disease is a solitary lesion where the lesion: \r\n** is palpable\r\n** size can be measured bi-dimensionally by tape, ruler or caliper technique, and\r\n** largest tumor diameter is at least 2.0 cm (that is considered measurable by the World Health Organization[WHO] criteria)\r\n* Note:\r\n** Patients with contralateral invasive breast cancer are not eligible\r\n** Patients with contralateral ductal carcinoma in situ (DCIS) are eligible\r\n** Patients with multifocal/multi-centric invasive breast cancer are not eligible; additional foci of DCIS in the same breast are acceptable Patients with recurrent breast cancer; patients with contralateral second primary breast cancers are eligible For patients with bilateral or multifocal/multicentric breast cancers, one of the following criteria must be met to enroll: (1) each cancer individually meets criteria for enrollment (only ONE tumor has to undergo central confirmation for HER2), OR (2) at least one tumor meets eligibility (per tumor size/nodes/subtype outlined above) and the other foci in the ipsilateral or contralateral breast are also HER2-positive but are too small for enrollment (e.g., a patient is eligible if a cancer is T2N0 and HER2-positive in one breast, but the contralateral breast has a T1b HER2+ cancer that isn’t eligible on its own, OR, (3) at least one tumor meets eligibility and the other foci in the ipsilateral or contralateral breast are HER2-negative and do not meet criteria for adjuvant chemotherapy per provider discretion (e.g. if a patient has a HER2-positive tumor meeting eligibility but also has a second, HER2-negative, small, node-negative, ER+, low grade cancer present, she is still eligible for enrollment); however, in the specific case that a second breast cancer is stage III and HER2-negative, that patient is excluded (because the second cancer is high-risk and likely will require non-HER2-directed therapy) Patients with stage III, HER2-negative cancer in the contralateral breast Prior radiation therapy or implant in the contralateral breast Surgeon’s opinion at the time of surgery that the subject’s well-being (e.g. significant comorbidities, intraoperative findings of a higher stage cancer or other independent acute health problems) would be compromised; if the contralateral breast is undergoing a nipple-sparing mastectomy with reconstruction as well, then the contralateral breast can be studied so long as there is no compromise to any element of their care History of any prior (ipsilateral and/or contralateral) invasive breast carcinoma History of DCIS and/or lobular CIS (LCIS) that was treated with any form of systemic chemotherapy, hormonal therapy, or RT to the ipsilateral breast where invasive cancer subsequently developed. Participants who had their DCIS/LCIS treated with surgery only and/or contralateral DCIS treated with radiation are allowed to enter the study Patients with a history of ipsilateral DCIS are eligible if they were treated with wide-excision alone, without radiation therapy; patients with a history of contralateral DCIS are not eligible Patients with synchronous contralateral invasive breast cancer are excluded Any previously treated contralateral invasive breast carcinoma or synchronous contralateral breast carcinoma Contralateral hilar node involvement Invasive cancer or DCIS in the contralateral breast Advanced (T1N1-4/T2-3 N any) invasive cancer in the contralateral breast Synchronous or previous contralateral invasive breast cancer; (patients with contralateral DCIS not treated with radiation are eligible) Untreated extensive stage (ES)-SCLC, defined as those patients with extrathoracic metastatic disease, malignant pleural effusion, bilateral or contralateral supraclavicular lymphadenopathy, or contralateral hilar adenopathy Previous (required active treatment within 5 years) or concomitant malignancy except basal cell cancer, in situ carcinoma of the cervix, or contralateral breast cancer. Subjects with a prior contralateral breast malignancy can be included if they did not receive any chemotherapy. No history of prior or concurrent contralateral invasive breast cancer; benign breast disease, LCIS or DCIS of contralateral breast is allowed Patients with a history of prior (ipsilateral [ipsi]- and/or contralateral) invasive BC Prior ipsilateral breast cancer radiotherapy will be excluded; prior contralateral breast cancer therapy within 2 years will also be excluded Qualifying cytological atypia in RPFNA, Masood score of 14-17; the qualifying RPFNA (of one or both breasts) must be send to Dr. Seewaldt's laboratory for cytological scoring and proteomic analysis; score results must be received from Dr. Seewaldt’s lab prior to patient registration/randomization; test must be done =< 90 days prior to registration/randomization\r\n* Note: Only the contralateral breast can be aspirated in women with DCIS and those undergoing surgery for an atypical lesion; the decision to aspirate the contralateral breast is at the discretion of the woman’s surgeon History of prior breast cancer-specific therapy within the previous 2 years; previous unilateral radiation in women scheduled for mastectomy of the contralateral side is allowed Prior radiation therapy to the contralateral (unaffected) breast Prior history of contralateral (unaffected) breast augmentation with breast implant placement Patients with previous contralateral invasive breast cancer treated with anti-cancer therapy are eligible Patients with synchronous ipsilateral invasive breast cancer or any prior history of ipsilateral invasive breast cancer; (patients with previous ipsilateral/contralateral DCIS or previous contralateral invasive breast cancer treated with anti-cancer therapy are eligible) Biopsy confirmed benign calcifications in at least one breast (same or contralateral breast)